However, he will certainly need Edinson Cavani to be on form against Dnipro on Thursday night in the Europa League.
The Partenopei, among the early leaders in Serie A, have suffered a serious lull in form both at home and abroad while Cavani has been sidelined through injury.
The Uruguayan is fit again, but Mazzarri's men are now six points shy of Group F leaders Dnipro, who emerged 3-1 victors in October's reverse fixture, and the Napoli boss is determined to close the gap with victory.
He told a pre-match press conference: "This team is not dependent on Cavani, we lost without him at Atalanta but there were a lot of players who came close to scoring.
"There is a lack of clarity given that we're playing every three days, but they are creating a lot of chances and just haven't had the luck to convert them.
"(Salvatore) Aronica and (Eduardo) Vargas will definitely play against Dnipro tomorrow [Thursday].
"We have to be more cunning, but more solid, and we need to pay more attention to the details.
"To the fans, I will just say that they need to stay behind the players right until the game is finished, and then they can whistle."
Midfield schemer Gokhan Inler added: "We have improved a lot, and tomorrow [Thursday] we want to show that we can still do well in the Europa League.
"(It) is not over yet and we want to prove that we can be there right to the very end.
"Our mentality is to always go out on the pitch with the will to win, that's what the boss wants."
Dnipro, meanwhile, are in search of four wins from four outings and qualification for the knockout rounds with two games to spare.
Success at the San Paolo would be no mean feat, though, as the Ukrainian side are unbeaten in 15 European home games, a run stretching back to December 1994.