Goals from Yaya Toure and Carlos Tevez saw the defending champions seal victory at the Etihad Stadium and close the gap between themselves and Manchester United to 12 points.
Only 11 games remain in the Premier League schedule but the Italian manager insists that it is not in his team's nature to give up on the title race.
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Joe Hart responded to his manager's recent criticisms by denying Frank Lampard from the penalty spot after bringing down Demba Ba with the score poised at 0-0.
Mancini praised Hart for the save and backed him as the best goalkeeper in England but warned that he should continue to improve his game.
"If they score the penalty, we still had a chance to win because we had another 40 minutes," he continued.
"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."