The champions' 2-2 draw with Liverpool on Sunday coupled with United's win over Fulham a day earlier has left Sir Alex Ferguson's side with a comfortable gap at the top of the table.
However, City chased down an eight-point deficit to win the title last season and still have to face the Red Devils at Old Trafford, where it won 6-1 in that campaign, filling Hart with hope.
"Of course we still feel we can do this," he told reporters. "That's who we are, and that's what we are. We've put ourselves in a worse position than we would like to be, but that's football sometimes.
He added, "The only time we can have an impact on them is when we play them. They do what they do, and I'm sure they have realized that if they play well they have a very good chance, but we know that we will always be there."
Sergio Aguero rescued a point for City against Liverpool with an incredible finish after Pepe Reina's error, while Hart preserved the draw with a close-range save from Daniel Sturridge in the game's dying embers.
"You could say it was a good result for us in the end – it was a tough one," the England No.1 stated. "You want to win, but we went behind and Sergio has had to pull something out for us to get a result. He didn't have any impact on the game whatsoever, but that's what great players do, and he scored a goal that counted.
"I hope it [Hart's save] can help keep us in the title race."