City took advantage of a rare missed penalty from Frank Lampard to claim a 2-0 win at the Etihad Stadium and reduce Manchester United's lead at the top to 12 points.
Superb goals from Yaya Toure and substitute Carlos Tevez in the last half-hour also strengthened City's grip on second place ahead of the third-placed Londoners. But with just 11 games remaining it seems unlikely City will retain their title, even though Mancini has vowed to fight on.
Mancini said: "I think for us now it is not important to look at the table. Only to continue to work like today, to play well, to improve and to look at the table in one month, 40 days.
"In football, it is finished when it is finished, the last minute of the last game. If we arrive at four games to go with United 12 points ahead, it is finished but I think our job is to continue to work."
Mancini, who began his post-match press conference by thanking outgoing pope Benedict XVI for his eight years' service, recognised Lampard's penalty as the game's pivotal point. After being outplayed for the first half, Chelsea could have gone ahead in the 51st minute after Joe Hart brought down Demba Ba.
Lampard had scored his previous 10 spot-kicks but Hart redeemed himself to save superbly and deny his England colleague his 200th Chelsea goal.
Mancini, who criticised Hart this week in light of recent mistakes, praised his goalkeeper for recovering from his error. Mancini said: "I say to him everything when he did a fault.
"I think we can't concede a penalty like this with a kick (long ball) from 45 metres - he and Kolo (Toure) both did a mistake. But after, it was fantastic. I think it was important. Maybe the game could have changed, but also if they scored, we would have had another 40 minutes.
"We were playing really well and we could have a chance to score other goals."