The now-retired Togo striker returns to the Emirates Stadium for the first time on Saturday since his controversial £25million exit from Arsenal last summer, and the first time since his stormy appearance against the Gunners earlier this season.
Adebayor was handed a four-match ban for raking his studs down the face of former team-mate Robin van Persie, an action which drew an angry verbal response from the Dutchman.
That incident would have been bad enough had it not come straight after an ill-advised goal celebration from the forward, when he raced the full length of the field to slide right in front of the Gunners' supporters after scoring against his old club.
As someone who was not even at Manchester City at the time, Mancini can look back at the incident from a detached perspective.
However, with points now vital in the battle for fourth spot, the Italian accepts Adebayor cannot afford to let himself get sidetracked again.
"I remember the game against Arsenal. I watched it on TV," recalled Mancini.
"I don't know why it happened but in that first game Emmanuel made a mistake.
"On Saturday it is important he only concentrates on Manchester City because Emmanuel is important to us when he is doing that.
"If he scores another goal I will be happy but it is important we don't have another situation like the first one."
Even though Arsenal's title challenge came to a grinding halt thanks to Wigan's astonishing comeback at the DW Stadium on Sunday, Mancini is equally certain the Gunners players will not have their minds set on revenge either.
There is a suspicion that Adebayor could be targeted, but Mancini insists that will not happen.
"The Arsenal players will not try to target Emmanuel," he said.
"He was banned for four games and that match is finished now.
"The Arsenal players are very professional. It is important everyone thinks about the game."
Adebayor has a personal need to impress that goes beyond inflicting more misery on Arsene Wenger.
Yet again this week City have been at the centre of rumours about a big-money summer bid for Fernando Torres.
The Blues have been heavily linked with Torres for a number of months now and it is anticipated they will make a bid for the currently injured Spain striker once the season is over.
Mancini insists he has not even thought about the matter. However, the Blues chief does accept he will face competition if he does make a move.
"Fernando Torres is a fantastic striker," said Mancini. "But all the teams in Europe are interested in him.
"We must get the rest of the matches out of the way first, then we will decide about other players."
Having failed to land a couple of other high-profile targets in Kaka and John Terry, City are aware they need to offer high-class competition as well as huge salaries if they are to lure the best players to Eastlands.
"All the top players want to play in the Champions League," added Mancini.
"Next year we want to be a team who wins the Premier League. To do that we need top players."
Whether that number includes Craig Bellamy remains to be seen.
The Welsh firebrand is said to have a stormy relationship with Mancini and Tottenham boss Harry Redknapp is supposedly monitoring the situation.
Yet Mancini is adamant there are no ongoing problems with Bellamy, claiming if a rift did exist, it would be obvious to everyone.
"I continue to read that I have a problem with Craig Bellamy," he said.
"This is false. I do not have any problems with him. If I did he wouldn't play.
I respect him. He works very well and always gives 100%."