Martin Skrtel appeared to handle the ball inside his own area in second half stoppage time as Manchester City suffered a damaging defeat in the Premier League title race
Goals from Raheem Sterling, Martin Skrtel and Philippe Coutinho saw the hosts resist an impressive comeback from last season's runners-up, though the defender appeared to handle inside his own area in stoppage time.
The City manager insists his side did not deserve to lose, but admits his players made "mistakes" and wasted opportunities to take the lead once they levelled matters in the second half.
"It's disappointing because we lost a game that we didn't deserve to," he told Sky Sports. "We played very well, especially the second half and the last 15 minutes of the first half.
"We had clear chances to score but football is made from good things and mistakes and we made a mistake and they won the game.
"They started very well, they scored a goal and after a corner they scored the second. It's easier when you're playing at home and you have gone two goals in front. Of course it's more easier to play with calm.
"After that we rearranged it and we finished the last 15 minutes of the first half with two clear chances. In the second half there was just one team on the pitch. We scored two goals, we had two or three clear chances to score [more goals].
"There was also a clear penalty. It totally hit his [Skrtel's] hand, very clearly, but we made the mistake on the third goal and they finished up winning the game."
Pellegrini's men have two games in hand on their title rivals and Pellegrini still believes that they can be crowned champions this season.
"Of course I said before the game that this is not the end of the Premier League," he told reporters.
"Liverpool have to play four games more, if they win 13 or 14 games in a row maybe they deserve to win the title, but we are going to continue fighting to the end.
"We play on Wednesday [against Sunderland] one of our postponed games, we can be just one point behind point behind Liverpool ... if we win those two games [in hand], and they have to play Chelsea against Liverpool."