City - fourth in the table ahead of Monday's trip to Crystal Palace - face an uphill battle in their bid to retain their crown after falling nine points behind leaders Chelsea with eight matches remaining.
Manuel Pellegrini's men have lost two of their last four league matches - against Liverpool and Burnley.
But City goalkeeper Hart has not given up hopes of lifting back-to-back titles, pointing to City's late surge last term, which saw the club edge Liverpool for top spot after winning their five remaining fixtures.
"We will never give up. It's kind of how we do it. We like to do it a different way," Hart said.
"We've not necessarily reached the standard week in, week out that we wanted to, but the beauty of football is that you get another chance – and that starts on Monday.
"We've proved it and the fans have proved it. That is one thing that is part of Manchester City, which we've taken with us from the olden days. We'll never give up while anything is possible."
Hart added: "We'll go for it. We know that the way we won the league the first time [in 2012] set a DNA.
"We have definitely moved on as a team since then. That was a massive achievement, but now we expect it of ourselves.
"We have been disappointed at certain times this season, but there are eight games to go and we'll give it all we've got.
"We've got some massive games - eight big games to reach a level that we need to reach.
"We've not necessarily done that all season, but we feel we are in the right place now.
"We have a lot of rest time and there are no excuses. Everyone is fit and ready to go."
