The visitors shipped four goals inside the opening 25 minutes at the Etihad Stadium and conceded a further two after half-time in crashing to their heaviest ever Premier League loss.
The final scoreline was the worst of Sarri's coaching career and comes less than two weeks on from the dire 4-0 defeat at Bournemouth, which magnified the scrutiny of the Blues' development under the former Napoli boss.
The Italian was probed as to whether his job could be in danger during a post-match interview with Sky Sports and admitted talks with the club's hierarchy are likely to be held, though he stressed that was a "normal" outcome after a game.
"I think that is right. I am in charge of the team and so it's right," Sarri said.
"I don't know at the moment, but I think that [talks] will happen. It's normal. Something we have to do."
Pressed as to what those talks could mean for his tenure, he added: "You have to ask the club. I have no idea about this at the moment.
"I am worried about my team. I am worried about the performance but my job is always at risk so I am not worried about the club. You have to ask the club."
Sarri appeared to ignore City boss Pep Guardiola at the final whistle and did not shake the Spaniard's hand before heading straight down the tunnel.
Asked about the incident, Sarri said: "I didn’t see him at the moment but of course as usual I will go to say hello to him later as usual. It was by chance because I wanted to go to the dressing room and at the moment I didn’t see him. I have not a problem with Pep."
Sarri admitted the mauling suffered against Guardiola's men was difficult to comprehend.
"It was really very difficult not to give them space and so we were in trouble, but I am not able to understand because as I said before in the week I had a very good feeling," he said.
"I think that we made a lot of mistakes against the wrong opponents. They played fantastic football and we made a lot of mistakes."