Chelsea suffered a shock 1-0 defeat away to struggling Birmingham – their third loss in four Barclays Premier League matches.
It means they now only lead Manchester United on goal difference, have netted once in four games and look shaky in defence in the absence of injured captain John Terry who has a back problem.
The Blues have suffered successive defeats, against Sunderland and Alex McLeish's side, since the departure of Ray Wilkins who is now claiming unfair dismissal.
Ancelotti knows the pressure levels will be cranked up after Chelsea suffered back to back league defeats for the first time since May 2006 courtesy of Lee Bowyer's first-half goal.
But he is adamant there will be no cause for alarm if Chelsea repeat the performance shown at St Andrew's when they were frustrated by inspired City goalkeeper Ben Foster.
Ancelotti said: "We got a positive reaction after the Sunderland game.
"We played good football, we played for 90 minutes with good spirt and with a good attitude.
"I don't have to say anything to my players. We were disappointed with the result at Birmingham because we deserved to win.
"But we have to stay confident and look forward to the next game. It is a difficult moment but we don't have to lose confidence.
"We were unlucky but we have to know this is football and these things can happen
"It was a fantastic performance by Foster. He saved a lot of opportunities from us and congratulations to him.
"But it is important to maintain belief in our play, in our quality, in our ability.
"If we are able to play like at Birmingham every game, with this attitude, I think we can win. The problem is to play every game like that."
Ancelotti gave his backing to striker and captain Didier Drogba Drogba who forced two fine saves out of Foster and hit the crossbar.
He has now netted only once in seven games but looked sharper after his bout of malaria.
Ancelotti said: "He was really different (to how he had been playing). He played a good match. He had a lot of opportunities. He was unlucky."
Of more concern to the Italian, was the fact Birmingham scored from their only worthwhile attack of the game.
He said "It is not good we lost the player who ran into the box (Bowyer)
"Maybe there was a mistake but it was just one during the game."
Ancelotti is hoping Chelsea are able to postpone surgery on Terry's back in addition to Alex who defied a knee problem to play against City.
He said: "We have to wait day by day. Alex needs to have surgery but he played without a problem on his knee.
"We have to wait the reaction of the knee. I think we can postpone the surgery and also for John Terry."
McLeish praised the contribution of former Leeds United midfielder Bowyer who has lost his place to Craig Gardner this season but seized his chance when the former Aston Villa midfielder was ruled out.
He said: "It was one of Lee's trademark runs off the ball which got us the goal. He has done that his whole life.
"He scored six goals in the first half of last season. In the second half it all dried up, not just for Lee but for the whole team.
"But, if you watch the games, he was still making the runs and just not quite finishing them off. It was a classic Bowyer goal against Chelsea.
"We haven't seen much of Lee this season and he hasn't been happy about not playing.
"But it was a perfectly timed run for the goal and he had the composure to finish it off."
McLeish added: "It was a marvellous result for us. I said before the game it was achievable but you never know with a marvellous outfit such as Chelsea.
"They have players who can turn the game in an instant and they nearly did it to us a few times.
"But we stood resolute, the players were fantastic in their commitment and determination. A great rearguard and a great keeper."
Patrice Evra claims Manchester United can make their rivals pay for their slip-ups and are on course to take over as the Premier League's outright leaders.
Evra scored his first goal since April 2007 as United saw off nine-man Wigan 2-0 with, in the words of Sir Alex Ferguson "a competent performance, but no more".
That was all United needed however, given the incompetence shown by Chelsea and Arsenal, and only goal difference is now keeping Ferguson's men from being top of the pile.
Evra said: "I said before the game that if we beat Wigan and Blackburn next week we would be top of the league, and I am still confident of that. But I think the team can give much more than we are giving right now. We are Manchester United and we need to be more aggressive and score more goals – and to bring back the way United play always."
Evra's headed goal arrived at the perfect moment just on the stroke of half-time.
Wigan self-destructed in the second half, shortly after Wayne Rooney had come off the bench for his first appearance since his controversial threat to leave the club was followed by the signing of a new contract.
Both Antolin Alcaraz and Hugo Rodallega launched into unnecessary challenges.
Alcaraz was sent off by referee Martin Atkinson for a second cautionable offence, while Rodallega was given a straight red for a two-footed, off-the-ground lunge at Rafael.
Javier Hernandez headed the second to leave Wigan stranded in the bottom three.