After failing to win in their opening two games of last season's competition before eventually being knocked out at the group stage, City were aiming to make a positive start to this season's campaign in what many have hailed as the toughest group in the competition.
Real Madrid dominated the first half with Hart making a string of impressive saves. However, the away side twice took the lead in the second period through goals from Edin Dzeko and then Alexander Kolarov just five minutes from the end. But late strikes from Karim Benzema and Cristiano Ronaldo completed a remarkable turnaround which Hart deemed unacceptable.
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"They're a very good team but so are we. We can't go 2-1 up and lose. You come to the Bernabeu and it's a great stadium, amazing manager, amazing players and we dug deep, we got a lead twice and we lost it so we can only blame ourselves."
The England international, noticeably angry with the result, was also unwilling to take positives from the game in the immediate aftermath, placing an importance on the outcome of the match rather than the team's performance.
He added: "It's hard to come off the field after losing 3-2 and be positive. I'm really sorry and I know you don't want to hear that.
"I'm sure in the coming days when we reflect we can see the good things that we've done but at the end of the day we've lost the game.
"We're not a team that should come here and pat ourselves on the back for doing well, we're a team that gets results."