Premier League - Mancini takes blame for defeat
The visitors put up a better fight in the second half but they failed to get a goal back and spurned the chance to move above Chelsea into third.
The Italian said that the players could have been better, but insisted he was at fault for the defeat.
"Probably we didn’t play in the first 20 minutes when Liverpool played very well," Mancini told Sky Sports. "But I think tonight I made a mistake, I did something wrong.
"I think the players could do better but I made a mistake.
"I want to apologise to the fans."
While Mancini took the blame, the former Internazionale coach refused to specify what the error was - although it can be assumed he was referring for the decisions to rest his midfield duo.
"It is for me to know, it’s not important," he said when pushed to pinpoint the error.
"Liverpool always start quickly, they are very strong at home and we conceded a lot of chances in the first 20 minutes.
"It was not because of the (FA Cup clash against Manchester United at the weekend) and we really wanted to win as it would have put us third."