That's it for tonight - don't forget to join us tomorrow for more Champions League drama.
Overall this display will be seen as a disappointing one, even though they have a glimmer of hope of escaping Group D.
City remain in the Champions League. But they need to win their final two games (against Real Madrid and Borussia Dortmund) and hope other results go their way.
Looking at the challenge on replays Van Rhijn definitely fouled Balotelli. It should have been a penalty.
Anyway, it's all over. Full time. 2-2.
Mancini and his players surround the referee and protest.
It looked like the referee was giving a penalty, but no.
Balotelli goes down in the box claiming his shirt was pulled but the referee blows the full time whistle...
This is it!
Man City win a free kick on the half way line. Hart will kick this into the Ajax box.
Boerrigter is off for Sana.
The corner is only half cleared and falls to Fischer whose shot flies wide.
Eriksen's fizzing effort forces Hart to push it over the bar. Corner to Ajax.
The crowd roars City on.
Three extra minutes.
Eventually Nasri's ball into the box towards Dzeko is gathered by Vermeer.
Into the final moments. Nasri's long ball finds Aguero but he can't find the room to shoot or pass.
Aguero thought he had won it, he has it in the net, but Kolarov is offside. No goal.
Poulsen goes off to be replaced by Viktor Fischer, who is making his European debut.
Kolarov's cross sees Dzeko grab a chance but he snatches at it and it goes wide.
Kolarov takes the corner but Kompany clears inadvertently.
Corner for City after Clichy's ball forces an Ajax clearance.
Aguero tries to find space in the box but he is denied and Ajax clear their lines.
Kolarov comes on for Barry.
Poulsen goes into the book for a foul on Balotelli.
De Jong can't get a header, he is beaten to the ball by Clichy. Good defending from City.
Van Rhijn's cross sees Kompany concede a corner.
Zabaleta flings it back in but again the ball is dealt with.
Nasri's cross is headed away by Blind.
Aguero is brought down by Poulsen near the byline. Free kick. Ajax put everyone in the box to defend this.
Ajax steam forward with Van Rhijn down the right, and his cross is only partially cleared.
Dzeko has a shot from distance but the low effort skims wide. Bit of a waste really.
Balotelli's goalward header forces a fine save from Vermeer.
Zabaleta wins a foul after Babel's late challenge catches him. Free kick in a dangerous position.
Schone goes off and Enoh comes on for Ajax.
Aguero is called offside as he arrives to challenge Vermeer for the ball. He doesn't look offside at all. Tough call for City.
A great tackle from Toure on Eriksen breaks up Ajax's attempt to get a passing move going.
Moisander is forced into a good challenge in the area as Zabaleta breaks free. Good defending.
Clichy's searching ball from the left looks for Balotelli but he handles as he attempts to control it. Free kick.
There is real hope in the stands now, and you can bet City will push for a third goal now!
A long ball is knocked on by Balotelli and Aguero gets between the defenders to hammer it home first time before grabbing the ball out of the net and running back to the centre circle.
De Jong hits it well and forces Hart into a diving save, Ajax have to settle for a throw. Strong armed save from Hart!
Toure drags down Schone on the edge of the box. Ajax freekick.
Heading towards the final 20 minutes. Still no massive urgency from City to find an equaliser.
Eventually Van Rhijn's cross forces Zabaleta to concede a corner which Hart punches away and Barry heads clear.
Ajax are giving City the run around as they look to find some space for a shot. They have been in possession for a decent spell now.
Edin Dzeko, the super sub, replaces Carlos Tevez for Man City.
Barry finds space on the edge of the box, after some good build-up, but his shot flies well wide.
Toure's cross finds Zabaleta, Blind picks up the loose ball but takes his time before clearing.
Ajax corner - real concentration on City faces. Eriksen plays it short and his cross is blocked. Better defending.
Eriksen dribbles his way through a host of City players and gets his shot off but it is wide. Danger averted.
Kompany has put in an assured, leader-like display in the second-half.
The Argentine striker wastes a golden opportunity. What is up with his boots?
Aguero breaks into the box and beats Vermeer to the ball but with the opportunity to put a ball across the goalline he slips. Massive error!
Balotelli turns and runs but Van Rhijn hustles him off the ball physically, but no foul. Well played.
We are approaching the hour mark at the Etihad and for all their pressure City need to create more chances and push the point.
De Jong decides to take a snapshot from outside the area which forces a parried but relatively easy save from Hart.
Ajax are dealing with the aerial bombardment well but they remain penned in their own half, their own area for long periods.
Toure finds room on the left wing and floats into the middle, but his cut back is cleared for a corner.
Ajax have been on the backfoot for the opening ten minutes of the second period.
Toure's kick hits the wall but after some penalty area ping pong Clichy chips in Aguero who finishes well, but he is offside.
This freekick is central, and looks like it will draw a shot from City.
Ajax are forcing City backwards but Aguero, Nasri and Balotelli combine to good effect and win a freekick.
Barry's drilled kick finds Nastasic with a free volley but it is too high and offers no danger to Vermeer.
They are being forced into errors and giving away needless fouls.
Tevez is next to get caught, on the edge of the box, by Eriksen. Are Ajax rattled?
Toure strides forward and slips in Aguero who is dragged down by Alderweireld who catches him on the ankle. Painful.
Aguero picks up on a stray pass and bears down on the Ajax goal but slips at the vital moment. Not the first time he has slipped tonight.
Vermeer comes to collect the freekick easily. No problems for the Ajax goalkeeper.
Blind goes into the book for the challenge. It was late and he catches him.
Immediately City win a freekick, Nasri is hacked down and looks in some pain.
That is a clear sign that City are going for it. They have to go for it!
Man City sub - Mario Balotelli replaces Javi Garcia
There was a strangely subdued atmosphere from the home crowd in the first 45 minutes. The Ajax fans had lots to sing and bounce about though.
We're getting ready for the second-half here. Will City give their fans something more to cheer about?
Vermeer paws the ball away and the whistle goes for half-time.
City win a corner - one last chance this half.
Ajax press high in a bid to see out the final moments of the half.
Roberto Mancini looks like he may be sucking a lemon on the touchline. Obviously planning his half-time team talk.
Aguero, Tevez and Nasri have run their socks off in this first-half but they will come away frustrated.
City are piling forward really looking to find another chance before the break but some dogged defending by Ajax allows them to keep the hosts at bay.
A searching ball finds Toure in the box but his downward header has no power or pace. Easy take for Vermeer.
From the throw Nasri and Barry are cornered and Ajax come away.
Toure wins the ball from Ajax and Nasri picks it up allowing City to win a throw in a good position.
Eriksen finds room on the right but his cross is long and floats out of play. An excellent build-up by Ajax is wasted.
They soon regain the ball and are knocking the ball around with style. Ajax on top as it stands.
Ajax are stringing the passes together but their attack comes to an end via a Kompany header.
City come off worse in the midfield battle allowing Poulsen to play in Babel who dribbles off and slips in De Jong but his shot is tame.
Eriksen finds space and plays Babel through one-on-one but he is offside. Let off for City.
Well spotted by Garcia, City are creating opportunities but they need to score.
Nasri and Aguero combine on the left allowing Garcia to cross but Zabaleta's header is saved well by Vermeer.
Aguero feeds Gael Clichy whose left-wing cross is batted away easily.
Ajax are not being given the opportunity to get their foot on the ball and dictate the play in any way - City are determined to push forward.
Cleared off the line - City's patient build-up play is capped off by Zabaleta breaking into the box and crossing for Barry who can't quite reach the ball and it is headed away. Close.
A Babel cross flies over the head of Schone and drifts into touch.
For all their intent City are finding it hard to break down Ajax's stubborn midfield.
City have some energy back about them now and are attacking with verve.
Yaya Toure chests down a cross from the right and swivels before volleying past Vermeer. They stand a chance now.
Aguero runs at the Ajax defence but loses his footing and the visitors come away with the ball.
Mario Balotelli is warming up already. City could use all the firepower they have got tonight as it stands.
City's corners aren't as effective as Ajax's and the ball is headed to safety.
Toure knocks the ball to Tevez on the right wing whose cross causes mayhem in the Ajax box but they clear it for a corner.
There is no marking from City, Joe Hart shakes his head in bewilderment and the City crowd are silenced. 2-0 to Ajax in less than 20 minutes.
Corner to Ajax.
Ajax are doing a great job of sitting back and making life difficult - it is up to City to find a way through and get on level terms.
A long ball forward sees Schone nearly go through but the ball is too high for him to bring down, he's no Luis Suarez.
Ajax are content to defend deep and hassle City when they get on the ball. It is working well currently.
They win a corner which is taken by Barry and Nastasic gets a shot in at the back post but Vermeer saves easily.
City are back on the attack again but they are being crowded out by Ajax shirts.
City get caught sleeping from a corner, fail to clear their lines and allow De Jong to tap in from close range. Major upset.
City are looking dangerous in the opening ten minutes here, refusing to let Ajax settle into their game.
Zabaleta makes the most of some patient build-up play and breaks into the box on the right but his shot goes over. Unlucky.
Poulsen brings down Barry on the halfway line after the City man wins the ball. City are having joy winning the ball in midfield.
Ajax not in a hurry to get rid of the ball from defence and they are nearly caught out but they come away with the ball safely.
Barry's corner is collected easily by Vermeer.
Toure wins the ball on the halfway line and City break in numbers but Aguero's shot from the edge of the box is deflected over - corner to City.
Every time Vermeer is given the ball City hastily close him down - a real sign of intent from the attacking players who are up for this.
And it has to be said when they are given time on the ball Ajax are knocking the ball around with great poise and technique.
Surprisingly Poulsen, calm on the ball, swivels and leaves Toure on the deck. Great skill.
City have started on the attack - Toure breaks into the box and goes down but the ref waves the protestations away - no penalty.
Aguero finds Nasri whose attempted shot is blocked.
A first couple of touches for Ajax keeper Vermeer and Samir Nasri closes him down energetically giving him no time to settle
Early attack down the left for Ajax with Ryan Babel but he is crowded out by defenders