Hart said the English champions had surprised themselves "in a very bad way" after they posted a fifth straight result without a win in Europe. Sergio Aguero's leveller after Karim Benzema's opener was not enough and they must now look to the Europa League.
"It's incredibly disappointing," Hart said on Sky Sports. "It's incredibly frustrating. We're a very good team and we've surprised ourselves in a very bad way. We weren't able to do the business when it mattered.
"All games have cost us. We've lost two away games and drawn at home. We led in the away games and lost. It's been a bad campaign for us."
Madrid's opener came when Maicon went to sleep at the back post, allowing Benzema to drift in unmarked to score. It was yet another avoidable goal for City to concede and Hart was not happy.
"It was a free man, seven yards out, sloppy," Hart said.
The frustration boiled over in the City keeper, who targeted the referee for allowing Madrid to time waste, but clearly Hart was just hitting out after another shocking campaign in Europe under Roberto Mancini.
"The ref's not had the best night. I'm not usually one to blame officials, but the ball's out of play for 20 minutes, I'm surprised at them for doing that," Hart said.
"But we're out of the competition."
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