Compared with the most regular English representatives in the continent's premier club tournament, the Sky Blues have the worst loss percentage, and by some distance, with 13 of their 30 games ending in defeat.
However, Hart says he is optimistic about his side's chances in the Champions League and hopes to carry their domestic success into Europe.
"We are moving in the right way. But we've got to have the mentality that we want to win the competition -- that's the only mentality we can have," Hart told the Daily Telegraph.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"There's no point in looking to get to a certain point and then thinking, 'it doesn't really matter now'."
"We've got to be focused. We are fighting in one of the toughest divisions in the world and we are up and around the top of it, so there's no reason why we can't be competing on the European stage."
City travel to Turin on Wednesday to take on Italian champions Juventus, who won the reverse fixture on Sept. 15, knowing a win would guarantee them top spot in Group D.
"We are realistic that a draw is a good result for us -- a win or a draw -- but we are going to turn up with every intention of winning the game," Hart said.
"Games turn out differently, especially in the Champions League, and you need a back-up plan at times. But we will go there hoping to have the group sewn up by the last home game."
(Reporting by Shravanth Vijayakumar in Bengaluru. Editing by Patrick Johnston)
