Sergio Aguero scored his 11th Premier League hat-trick to equal Alan Shearer's record, with Raheem Sterling adding a double and Ilkay Gundogan also on target in Sunday's rout at the Etihad Stadium.
Chelsea have conceded 12 goals in their last three Premier League away games, their battering at new league leaders City coming on the heels of a 4-0 thumping at mid-table Bournemouth.
Chelsea captain Cesar Azpilicueta apologised for their showing after the Blues slipped to sixth in the league and Sarri also acknowledged their performance was unacceptable.
"I am doing my best and I'm trying to get the players to do their best but at the moment I can only say sorry because in the last three away matches we played very badly," he said.
"It's very difficult to describe our performance. It's also very difficult to understand because during the week I really was very happy with the team. My feeling was very good yesterday in the meeting and the warm-up today.
"We started well but we conceded the first goal in a stupid way in the fourth minute and then everything was really very difficult because we had to stay in the match but we weren't able to do that.
"The reaction was not very good. In the 20 minutes after the first goal we made a lot of mistakes against the wrong opponents who played fantastic football.
"I am surprised because at the beginning of the season we played better away than at home. I don't know what's happened but at the moment we're in trouble.
"In the last three or four matches we have been in trouble without a reaction at the first difficulty so we need to understand."
Sarri told Sky Sports he expects to hold talks with the club's board after their historic loss and in another post-match interview he gave an insight into his relationship with Abramovich.
"If the president calls, I'll be happy, seeing as I never hear from him," Sarri said to Sky Sport Italia. "To be honest, I don't know what to expect.
"Manchester City play fantastic football and I saw an extraordinary team. We had a total blackout."