Superb goals from Yaya Toure and Carlos Tevez ensured the champions took advantage of a rare Frank Lampard penalty miss to reduce Manchester United's lead at the top of the Barclays Premier League to 12 points.
With just 11 games remaining it still seems an unlikely quest but the victory at least extended their advantage over third-placed Chelsea to seven points.
Mancini said: "In football, it is finished when it is finished: the last minute of the last game.
"I think our job is to continue to work."
City were superior and deserved their victory but it might have been different had Joe Hart been sent off for bringing down Demba Ba or not saved Lampard's subsequent penalty. Lampard was one kick away from his 200th Chelsea goal when he lined up a 51st-minute spot-kick after Ba beat Kolo Toure to a long ball and was clipped by Hart attempting to round the goalkeeper.
Yet after scoring his previous 10 penalties, in-form veteran Lampard was denied as Hart redeemed himself with a smart save. It was a good response from Hart after some criticism from Mancini in the week and the keeper admitted it was a save he "had to" make after the foul.
Mancini described Hart as "one of the best keepers in Europe" in a television interview and said he wants "his standards always to be high".
He was less forthcoming in his post-match press conference, praising him only in the context of correcting an 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 both did a mistake."
City capitalised as Yaya Toure opened the scoring with a superb curling finish from inside the area just after the hour and substitute Tevez added a powerful long-range strike after 85 minutes.
Mancini, who began his media conference by thanking outgoing pope Benedict XVI for his eight years' service, said: "We worked well this week. It was important to start well - be strong, don't concede anything."