Raheem Sterling struck the opener and Gabriel Jesus added a second as City appeared to cut through the visitors at will at the Etihad Stadium.
Dries Mertens missed a penalty late in the first half, though, and Napoli were much improved after the interval to make a fight of the Group F clash.
Sarri's men came up short despite Amadou Diawara converting a second spot-kick, but the coach took some positives from an entertaining encounter.
"I don't know what happened in the first 30 minutes," he said. "We gave too many spaces to a devastating team and they punished us.
"We were very poor, but we played very well for the rest of the game. Playing at same level of Manchester City for over an hour is already something.
"We managed to fight back and not many teams at the moment are able to come back in the way we did and cause difficulties for Man City.
"We regret the fact we missed the first penalty, but we know now that we are on the right path to be competitive in Europe as well."
Despite Napoli's recovery to almost claim a point, Mertens was still frustrated about his own missed first-half opportunity.
"We have proved that we can play at this level, but we are very angry - especially because we did not manage to play our usual game in the early stages and because we missed very good chances later on," he said.
"I missed the penalty and I had another good opportunity. I really should have scored.
"I'm more angry with myself than satisfied with our reaction, there's no doubt about that."