And although the Blues thrilled in a 3-0 opening-day win away to Huddersfield Town on Saturday, Sarri believes there is more to come.
Chelsea had to dig deep early on against Huddersfield, but went in at the break with a two-goal cushion thanks to N'Golo Kante and summer signing Jorginho.
After a frustrating debut against City, Jorginho produced a fine display at the base of Chelsea's midfield.
Maurizio Sarri feels Chelsea will continue to improve under his stewardship, but the club's new coach will not aim to repeat his winning formula from Napoli. "We play high, with a lot of possession of the ball, in a technical way".
"I wish him good luck at Real Madrid, but now we have to concentrate on Kepa because he's our goalkeeper".
"We're happy because to be honest our pre-season games were not that good", he said.
Eden Hazard also produced a lively cameo after coming on as a 76th-minute substitute, creating Chelsea's third goal, rounding off a near ideal start to life in English football for Sarri, who had predicted that his team would encounter problems with results and performances in the first half of the season.
But the game turned decisively towards the visitors when Chelsea doubled their advantage just before the interval as Marcos Alonso burst into the area and went down under challenge from Christopher Schindler.
- Chelsea midfielder Jorginho has scored 90 per cent of the penalties he has taken in the top five European leagues (all competitions), converting 10 of his 11 spot kicks across three different clubs (Verona, Napoli and Chelsea). I had a lot of time to take care of me past year, so now I'm 100 per cent.
"He jumped before the penalty and Ben (Hamer) had already dived so I don't know why the ref didn't make him retake the penalty".