City's hopes of retaining their crown look slim with rivals Manchester United holding a 12-point lead at top of the table with just 11 games remaining.
The champions boosted confidence after a run of three league games without a win by seeing off third-placed Chelsea on Sunday and Hart is determined to keep the dream alive.
The England goalkeeper, who saved a penalty from Frank Lampard in the 2-0 victory, said: "Even if there is one game to go and we are 12 points behind, we'll still believe. We've got to.
"We've got to keep fighting, you never know. We have just got to keep going.
"It's going to be really hard, we've got a lot to do but we're going to have a damn good go at doing it."
Manager Roberto Mancini was scathing of his players after a dismal and damaging defeat at Southampton just over a fortnight ago but Hart claims their spirit was never in doubt.
The 25-year-old, himself subject of individual criticism from Mancini since the loss at St Mary's Stadium, said: "We have got it, no doubt about it.
"We all under-performed against Southampton - that's gone, you can't do anything now, you move on from that. You have got to look forward.
"You can speculate and talk about the past but we have just got to look forward and try to win. The only way is up for us."
City are not in action again until they travel to struggling Aston Villa next Monday, by which time they could be 15 points behind United.
Mancini hopes captain Vincent Kompany will be fit to return after five games out with a calf injury which has taken longer than expected to heal.
Mancini said: "The calf is a strange injury, and it is very dangerous. I hope we can recover him for Aston Villa."
Midfielder Gareth Barry will hope to prove his fitness from an ankle problem while Mancini has also revealed right-back Maicon faces a month on the sidelines after a knee operation.
The Brazilian missed the Christmas programme and the whole of January with a knee injury but had made three substitute appearances this month.
Mancini said: "He has had surgery on his knee, but in a month he can recover. The operation was to clean his meniscus."
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