The City manager pin-pointed fatigue for their lacklustre display at Anfield, which followed losses to leaders Leicester City and Tottenham Hotspur, and left them 10 points off the top with 11 games remaining in their season.
City had played a gruelling 120 minutes against Liverpool before winning a penalty shootout in the League Cup final on Sunday and travelled to the Ukraine to play Dynamo Kiev in the Champions League last week.
“It is difficult to have an excuse but I saw the team was not recovered from the last week. We played Champions League and then League Cup final and I saw the team was not fresh and Liverpool played better,” Pellegrini told the BBC.
“The last two days we work very light, just try to recover the players but from the beginning they won all the balls and had a high pace - more pace than our team.
“We didn't attack well and create chances and didn't have fresh legs to play like we can.”
The Chilean, who is leaving the club in June to make way for Pep Guardiola, is unlikely to gain much sympathy from his Premier League rivals, given that City's squad is one of the most well-stocked in Europe.
The League Cup exertions also seemed to have little impact on Liverpool, who put in a sprightly display, full of aggressive, attacking football.
They took a two-goal lead into the interval with goals from Adam Lallana and former City midfielder James Milner and added to their advantage through Roberto Firmino after the break.
It was a small measure of revenge for Sunday's Wembley result for Liverpool boss Juergen Klopp, whose side have now completed an emphatic league double over City, having won 4-1 at the Etihad Stadium earlier in the season.
“The best word I could say that would describe this was... 'boom!',” the German coach told BT Sport.
“Wow. What was this? It was really good to be honest. It showed us what these boys are capable of and it was a really good performance.”
The result lifted Liverpool up to eighth in the table, but they remain six points shy of fourth place City in the hunt for a Champions League qualification place.– Reuters
Original source: Pellegrini blames fatigue