The two teams were evenly matched at 1-1 at the break on Sunday but then Liverpool took control of the game in the second half and claimed victory thanks to Philippe Coutinho’s 75th-minute strike.
Key to City’s demise was the inability of their two central midfielders, Fernandinho and Yaya Toure, to cope with Coutinho and Adam Lallana dropping deep to link Liverpool’s midfield and attack.
Pellegrini replaced striker Edin Dzeko with midfielder James Milner in a bid to stem the tide, but by then the momentum was with Liverpool.
Pellegrini told Sky Sports: “The formation was not the problem. The problem is that we lose too many points.
“We started to lose too many balls, and Milner played well when he came on. Dzeko worked very hard in the first half, so he had to come off.”
Despite Liverpool’s second-half dominance, Pellegrini insisted the quality of Jordan Henderson and Coutinho’s goals was the only difference between the two sides.
He added: “They scored two beautiful goals. It was impossible for Joe Hart to save one of them.
“The rest of the match was even. We also have many chances. It was a close game, but they won because they scored two beautiful goals.”
The result means City remain five points adrift of Premier League leaders having now played a game more, and Pellegrini admitted his side’s chances of retaining the title had diminished.
He said: “We have three points less, and if we drop points, it makes it more difficult. We must try to win our next game, and then at the end of the season we will see.
“It is important to maintain our level of performance and not make mistakes on the ball like we did today for the first goal.”