Carlos Tevez's excellent second-half winner proved the difference between the teams on Saturday and lifted City to within four points of their opponents, who remain top of the table.
City boss Roberto Mancini claimed on Friday Chelsea would retain their title "easily" and continued to tip them for glory in May after Saturrday's game, but Ancelotti expects a genuine challenge to come from his fellow Italian's team.
"They are fantastic players, a very good squad. They can fight for the title," he told Match of the Day.
Next up for Chelsea is a Champions League clash at home to Marseille before they take on Arsenal at Stamford Bridge and then travel to play Aston Villa at Villa Park, where they lost 2-1 last term.
But Ancelotti did not seem too concerned to be heading into those games on the back of a first defeat of the season.
"We lost also last year here, it's not a good pitch for us," he said. "But we stayed at the top of the table, every game is a big test for us.
"Strange performance, but it can happen you are not able to score, this is football.
"You have to play against a strong team with a good performance. If you don't play at your best it's normal you don't score a goal."
Chelsea went into the game having scored 21 goals in their opening five league games but were unable to break down a well-organised City defence.
Ancelotti even took off leading striker Didier Drogba in the 75th minute, bringing on Daniel Sturridge, a sign of how little joy his side were having up front.
And he admitted his opposite number had got his tactics spot on.
"We didn't play how we wanted. We suffered the pressure in midfield that Man City put on us," he added.
"They won a lot of tackles in midfield so we conceded a lot of counter-attacks.
"We were not able to use speed in our play because there was no space.
"We played too complicated in the opponents' half so we didn't have a chance to score.
"I think that they used a good tactic to play against us. They wanted to do counter-attacks and they did some counter-attacks very well, very quick."