City scored four times inside the first 25 minutes to inflict Chelsea worst loss in any competition since 1991 and a 4-0 defeat to Bournemouth in their last away game was Chelsea's heaviest league defeat since 1996.
Sarri's side remain outside of the Premier League's top four and the club's supporters have questioned some of his tactical decisions.
"I don't know. You have to ask the club," said the Italian when asked if he feared being fired just eight months into a three-year contract at Stamford Bridge.
"I am worried about my team, worried about the performance but my job is always at risk."