The hosts dominated the opening exchanges but the game remained goalless at half-time. City took the lead through Edin Dzeko after the break before Marcelo equalised for Los Blancos. Aleksandar Kolarov again gave the visitors the lead with just five minutes remaining.
However, goals from Karim Benzema and Cristiano Ronaldo completed a dramatic turnaround for Madrid and Mancini admitted his disappointment at the nature of the defeat. He also stated that the defeat was a result of his side conceding too much space to the home side, rather than a lack of application.
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"We didn't lose concentration, we went too deep with the team and this is the only mistake.
"I think that we went too deep throughout the team and we conceded more space for them and I think that this was a mistake.
"At the moment we are disappointed but I think that everything will help us to be stronger in the future."
The 47-year-old also believed his side suffered from bad fortune during the game in the form of injuries to two of his players, which in turn affected his ability to make tactical changes.
He added: "I think that we were also unlucky because we lost two players through injury, Nasri and Maicon, and we had a problem because we wanted to change Aguero because we wanted to attack more, but instead we lost this change."