Sergio Aguero and Aleksandar Kolarov gave City a 2-0 lead but Villa fought back through goals from Tom Cleverley and Carlos Sanchez to level the score at 2-2 before Fernadinho grabbed an 89th minute winner.
Pellegrini, whose side moved up to second in the Premier League, acknowledged the visitors deserved credit for their performance, but was full of praise for his side???s character after the late victory.
“We played against a team that played very well,” he told Sky Sports.
“Maybe for our team it was one of our worst games of the season in possession. We lost so many balls during the game that it was very easy for Aston Villa to have possession of the ball.
“So many games we have 70, 75 per cent of possession and we lost.
“I think today we didn’t play so well but we have spirit to fight, to try to win – you see this in the last five minutes when they (equalised).”
Minutes before Fernandinho???s winner, Christian Benteke was tripped by Joe Hart in the penalty area but City were fortunate to see the linesman???s flag go up for offside.
However, Pellegrini did not believe his side should have been reduced to 10-men and thought his side could have been awarded two penalties.
He said: “I think there was an offside of the linesman. I think we have also two clear penalties in their box – one for Aguero.
“I don’t think (we were fortunate).”