City take on Dynamo Kiev in the first leg of their last-16 tie in the Ukrainian capital on Wednesday.
Beating Kiev would take City into the quarter-finals for the first time but goalkeeper Hart feels the key to success is believing the team can go all the way.
The England number one told the club's website, www.mcfc.co.uk: "We've got to believe that (City can win it), or else there is no point in turning up on Wednesday.
"We've got to believe that we've got what it takes
You know, it's the best of the best, and if you're not at your best you will lose, simple as that, in this competition
So it's all about peaking for the game and being in the right place at the right time.
"It's an amazing competition
It's something we really look forward to as a team
But we're very lucky that we're involved in a lot of competitions.
"The majority of the time when it comes to the Champions League we're still fighting on all fronts, and this is a good time to be a Manchester City player and a good time to be fighting."
Hart's comments turn focus back to City's challenge for honours after the controversy over their selection for Sunday's FA Cup fifth-round tie at Chelsea.
Prioritising the trip to Kiev and next Sunday's Capital One Cup final against Liverpool at Wembley, manager Manuel Pellegrini fielded a weakened side at Stamford Bridge and saw them beaten 5-1.
Because of a lengthy injury list, Pellegrini did not want to risk the fitness of any more of his senior stars having planned to travel to Ukraine on Monday.
City did train prior to their departure and defenders Eliaquim Mangala and Bacary Sagna were both involved, raising the possibility they could be back in contention in Kiev.
Kevin De Bruyne, Jesus Navas, Samir Nasri, Fabian Delph and Wilfried Bony remain on the sidelines.
Source : PA
Source: PA