Goals from Yaya Toure and Carlos Tevez gave the defending champions victory at the Etihad Stadium, where Joe Hart also saved a penalty from Frank Lampard.
City still trail neighbours Manchester United by 12 points but have not given up hope with 11 games remaining.
"We can't think it's finished with 11 games to go," manager Mancini told Sky Sports. "It's not my mentality or the mentality of the players."
Hart brought down Demba Ba to concede the 50th minute penalty but redeemed himself with an excellent save to deny Lampard what would have been his 200th Chelsea goal.
"If they score the penalty, we still had a chance to win because we had another 40 minutes," added Mancini, who has been critical of Hart in the past couple of weeks.
"I think Joe is the best in England and one of the best in Europe and I am pleased for him because he saved a penalty.
"But he could do better before with the long ball; he could be perfect if he wants to."
Mancini added: "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.
"We worked well this week. It was important to start well - be strong, don't concede anything."
While the result may not prevent speculation over the Italian's future, it did not pile pressure on in the way defeat did for opposite number Rafael Benitez. Benitez's side were far from potent and the unpopular Spaniard was once again subjected to abuse from fans.
He continued to put on a positive face and joked when asked if he was tiring. Benitez, who put John Terry and Fernando Torres on the bench, said: "I was not running so I am fine. I am disappointed because we could not win.
"I am just thinking about the next challenge."
Benitez agreed the game hinged on the penalty, but was unsure if Hart should have been sent off. He said: "I haven't seen the replay, but (it should have been) at least a yellow card. You can argue he is going in this direction but it is still a clear chance.
"I think it was a turning point. It was a crucial moment in the game."