Sarri had two years left on his contract after leading his hometown club to challenge champions Juventus for the title last season.
But after Sarri asked for more time to consider his future, former Chelsea and Real Madrid boss Carlo Ancelotti was appointed as new coach of the Serie A runners-up.
The 59-year-old Sarri told Il Mattino: “We were having dinner … discussing whether or not to stay. We turned on the TV and we saw Ancelotti entering Filmauro (the headquarters of Napoli owner Aurelio De Laurentiis).
“I had some doubts, that’s fair, but there was a clause in the contract and it wasn’t something I had asked for. The timing wasn’t respected.
“Here it is totally different: it is an absolute party, it is a pleasure to arrive in the stadiums and see the fans with different shirts drinking a beer together.
“I sign autographs for the fans of the opposing team on the sidelines, before and after the match.
“There are games with so much intensity, physicality. The English game is a different football from the Italian one, played in extraordinary stadiums.
“But at the beginning, it’s not so simple to understand things. I know less about the teams I face and the opponents.”
It is the first time that Sarri, who started out as a banker, has coached outside Italy.
“Close up (life in Italy) is full of problems. But when we are far away, there is a bit of nostalgia and something is always missing.
“More than all the food, even though I’m getting used to the meat and salmon here. But I can’t find anyone who makes coffee like Tommaso (Napoli coffee maker).”