City lost 1-0 in Madrid on Wednesday evening to lose 2-1 on aggregate and exit the Champions League at the semi-final stage.
This season represents the Premier League giants best ever finish in the competition across the club’s entire history.
Hart, who made a number of important stops across both legs, believes City could have ‘easily’ gotten even further.
Speaking to BT Sport afterwards, he described Gareth Bale’s cross, which went down as a Fernando own-goal, as ‘very lucky’.
“We could easily be in the final but they managed the game well. They got a very lucky goal but it is what it is,” said Hart.
“We just did not have that little bit more. Aguero announced himself in the 88th minute, it was a good effort, but did we do enough over the two games? I don’t know.”
City rarely troubled Keylor Navas during the game, whereas Cristiano Ronaldo had a couple of great chances and Gareth Bale hit the woodwork with an impressive header.
City’s best chance fell to Fernandinho, who hit the post with a fierce effort shortly before half-time, while Sergio Aguero came close with a wonderful effort in the final ten minutes.
The club are currently fourth in the Premier League table and four points ahead of Manchester United, their cross-town rivals having a game in hand.