David Silva’s close-range finish and a Glen Johnson own goal in the opening 17 minutes of the second half cancelled out first-half goals from Raheem Sterling and Martin Skrtel.
If we win our two games in hand we will be a point behind Liverpool, who still have to play Chelsea. The title does not finish today
Luis Suarez was fortunate not to receive a second yellow after going to ground easily on a couple of occasions before Philippe Coutinho netted a 78th-minute winner.
Jordan Henderson was sent off for a high challenge in injury-time, and City manager Pellegrini admitted key mistakes cost the visitors three points.
“It was a very pretty match as it was two teams who like to attack. We deserved a better result. We are very unlucky,” Pellegrini told BBC Sport.
“We played very well second half when there was only one team on the pitch and we had clear chances to win the game.”
“They also played very well, especially the first 20 minutes. Normally, Vincent Kompany is great defender but today he made a mistake.
“There was just one team inside the pitch in the second half. There was a clear penalty when Martin Skrtel had a handball but I don’t think the result today was because of the referee, who had a good game.”
Pellegrini warned Liverpool that the title race is not over despite the Reds’s seven-point lead, with the Citizens having played two games less.
“If we win our two games in hand we will be a point behind Liverpool, who still have to play Chelsea. The title does not finish today,” Pellegrini added.
“We are still going to fight. A lot of things will happen between now and the end of the season.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news