Sarri’s side put the midweek disappointment of losing to Wolves behind them to get back to winning ways and bring City’s unbeaten start to the season to an abrupt end.
N’Golo Kante opened the scoring by firing into the roof of the net on the stroke of half-time.
David Luiz made sure of all three points with a deft header from Eden Hazard’s corner with 12 minutes left ion the clock.
That saw Chelsea move back in to the top four but they remain eight points off now-leaders Liverpool, who beat Bournemouth 4-0 at the Vitality Stadium to claim top spot.
And Sarri insists he has not set his sights on challenging for the title in his first season in English football.
“As I said, always as you know, I think the gap is impossible to cover this kind of gap only in one season,” the Italian said.
“One match – you can play one match, of course. Then in the competition of 10 months it’s very difficult to cover the gap.
“I think they are, at the moment, the best team in Europe.
City were made to pay for a host of missed chances, with Kante’s opener coming against the run of play.
“We won today. But we have to say we were a bit lucky in the first 25 minutes, because they could score,” Sarri admitted
“A little bit lucky in the first half and very good second half.”
“I’m happy for the win because it’s difficult to win against (Pep) Guardiola’s team.
“I know very well they are a step ahead now. We have to work to cover the gap.
“We are not sure to be able to cover the gap. We have to try, of course.”