Roberto Mancini recently dismissed City's chances of winning the Premier League for the first time, but Hart believes that it is all mind games from the Italian boss.
"There is no point in us turning up on Sunday if the title race is over. We've still got to believe, we've still got to fight for every single point available," said Hart.
"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."
City host United on Sunday with the Sky Blues sitting five points behind their rivals with four games left to play.