Mazzarri was dismissed towards the end of the first half in a volatile match, which was settled late on from the penalty spot by Edinson Cavani.
A hard-fought win away from home maintained Napoli's unbeaten record and moved them level on points with Juventus at the top of the Serie A table.
Mazzarri said at the post-match press conference: "There was a nasty foul right in front of me and I spread my arms to highlight how bad it was.
"The referee threatened me, then the fourth official told him to send me off. I prefer not to talk about it now."
Napoli continue their title charge with a home match against Udinese on Sunday, October 7.