City have now scored 33 goals in their last five home games in all competitions and have a chance of lifting their first silverware of the season when they face Chelsea again at Wembley in the League Cup final on February 24.
The reigning Premier League champions punished a poor Chelsea performance through a Sergio Aguero hat-trick, a Raheem Sterling brace and Ilkay Gundogan's strike. "It is hard to explain what happened", said Chelsea captain Azpilicueta.
"We are conceding a lot of goals and we can not accept that".
After the full-time whistle was blown, Rudiger was one of few players to front up to the fans, going over to the away support to apologise.
Their manager accepted he is concerned by their recent displays but gave a considered assessment when asked whether he fears for his future.
"I don't know", Sarri said. "You are asking me [about] something which is not my job".
However, not every fan was impressed with the gesture, with one hurling abuse at Rudiger for his - and the team's - awful performance. "You have to ask the club". "I've come to say sorry", the defender told them.
"I have to work for this because my target is to play my football".
"I didn't see my football (against City)".
There was no repeat of the lengthy dressing-room inquest between Sarri and his players that followed Chelsea's shock 4-0 loss to Bournemouth earlier this month.
Sergio Augero scored a hat-trick, after missing the tap in of the century, but Maurizio Sarri's side lost because they were out played across the board.
"I'm surprised because at the beginning of the season we played better away than at home so I don't know what has happened but at the moment we are in trouble", Sarri added. So now we need only to understand the reasons why at the moment it isn't working.
"It is hard to describe our performance, it's hard also to understand".
Pep Guardiola's team scored within four minutes and hit six in total past Sarri's hapless players in what City's manager later described as the best performance he had seen at the Etihad Stadium since he took charge. "We were not able to stay in the match and react later".
Pep Guardiola's side struck four times inside the opening 25 minutes and continued to attack a beleaguered Chelsea throughout as Maurizio Sarri's humiliated team shipped six goals in a Premier League match for the first time in their history.