City fell eight points behind United with defeat against Arsenal this month, but Sir Alex Ferguson’s side’s surprise defeat against Wigan meant the gap was reduced to five points with five games remaining.
Both teams recorded victories last weekend in the Premier League, with City taking on Wolves and United taking on Everton this weekend before the potentially decisive Manchester derby the following Monday.
While manager Mancini has previously admitted he believes the race is already over, Hart says City are continuing to fight ahead of the showdown at the Etihad stadium on April 30.
“There is no point in us turning up on Sunday if the title race is over,” the England goalkeeper told Sky Sports News. “We've still got to believe, we've still got to fight for every single point available.
"I don't think he (Mancini) means that the season is over. I think he is just trying to play it down a little bit and let us get on with what we need to do. There is no way any of us would give up until it is mathematically impossible.
"I know three of them definitely can be overturned - that is in our hands.
"Other than that, we've got to rely on other teams. We can only battle away and try and win every game and hope that United slip up."
The return of Carlos Tevez has inspired City in their last two games, with the Argentinian scoring four, including a hat-trick against Norwich, in their last two games.
Tevez spent five months in exile following his refusal to come in in the Citizens Champions League defeat against Bayern Munich in September.
Hart has praised the former Manchester United striker’s influence, and insists the controversy that surrounded him has been forgotten.
"We have been a bit dry on goals recently, so that fresh Carlos input has been awesome," he commented.
"You can say what you want about Carlos Tevez, but when he plays, he plays to win and he plays for his team-mates.
"There are far more important things in our lives than what went on and what didn't go on.
"We have that goal of trying to win the league and Carlos has bought into that. He has not come in and tried to make any big statements. We have just all moved on."