Chelsea now sit sixth in the Premier League, below Arsenal on goals scored, ahead of what could be a decisive period for Sarri before the end of February.
When asked whether he fears being sacked, Sarri replied: "I don't know, you have to ask the club".
Maurizio Sarri's reputation took another damaging blow less than two weeks on from the awful 4-0 defeat at Bournemouth with the Italian's team ruthlessly sliced apart at the Etihad Stadium.
"I am anxious about the performance, but my job is always at risk". "You are asking me [about] something which is not my job".
Sarri was back at work at Chelsea's Cobham training ground on Monday as he prepares the squad for their two-legged tie with Malmo, who they face in Sweden on Thursday. "We started well but after four minutes we conceded a goal in a stupid way".
Despite appearing a broken man as he slunk off down the town on Sunday, Sarri insisted that was not the case with his system, saying: "Today I didn't see my football".More news: 3 killed by US-led airstrike in eastern Syria
A poor header by Chelsea's Ross Barkley towards his own goal gifted Aguero with City's third, the Argentine firing home with a first-time shot on the turn, and then a low drive from Ilkay Gundogan made it 4-0 after 25 minutes.
"But I think, even this season against Liverpool at home, even though we just won 2-1, it was a fantastic performance".
"But Liverpool have relied a lot this season on what they've done defensively, the two Dutch players were outstanding at the weekend, [Georginio] Wijnaldum was back and certainly that man Van Dijk at the back what he's done".
Chelsea are making a nasty habit of breaking records for the wrong reasons under Maurizio Sarri, with time running out for the Italian to avoid becoming the latest coaching casualty at Stamford Bridge.
"We knew we had one of the best teams in front of us and we knew it would be tough".
The Russian has been absent from games this season, and Sarri revealed after the chastening defeat to City that he "never" speaks to his boss.
"We had only to stay in the match but the reaction was not good".