The Chilean's charges looked to be in the ascendancy after battling back from two goals down to level it up midway through the second half at Anfield.
But a poor defensive clearance from Vincent Kompany allowed Philippe Coutinho to curl home a late winner for table-toppers Liverpool, who now hold a seven-point advantage over City.
Pellegrini's men have two games in hand, however, and the City manager 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 said. "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."
First-half goals from Raheem Sterling and Martin Skrtel gave City a mountain to climb, but David Silva reduced the deficit in the second half before playing a hand in the leveller, his shot deflecting off Glen Johnson and Simon Mignolet on the way in.
At that stage, City looked to be heading for a crucial triumph and Pellegrini conceded that he expected them to win it from there.
"Of course (we should have won) because I think that the team played very well," he added. "Not only second half but the last 15-20 minutes of the first half we had clear chances to score. We didn't (score).
"Second half we drew (level at) 2-2 and we had other clear chances to win the game. Finally Liverpool won the game because of a mistake."
