The Partenopei have floundered in Serie A over recent weeks while their Uruguayan striker has been injured, both drifting away from league leaders Juventus and being leapfrogged into third by Inter Milan.
Ahead of Sunday's trip to Genoa, Mazzarri has once again rejected suggestions that his other forwards are lost without Cavani, who returned to lead a 4-2 comeback victory over Dnipro in the Europa League.
The 51-year-old told La Repubblica: "Once again it looked like everything was going against us, but with a great performance we triumphed over adversity.
"It is not true that we are dependent on Cavani. He scored four goals but his team-mates provided four unbelievably good assists.
"It's always down to the whole team, he just finishes off everybody's hard work."
Cavani - known as 'The Matador' - will hope to add to his seven league goals when Napoli visit the Stadio Luigi Ferraris in a bid to heap further woe on struggling Genoa.
Grifone president Enrico Preziosi put a four-game losing streak to one side to assure fans that the Ligurian club will not be relegated at the end of the season.
Preziosi moved to replace Luigi De Canio with Luigi Del Neri last month but the Rossoblu's subsequent form has taken a nosedive, leaving the club marooned in 17th place.
"I can assure you that Genoa will not go down to Serie B," said Preziosi.
"It's right that the fans are getting angry, but we need to react and put these bad times behind us.
"I understand the supporters, but it is important that we feel them close to us at the moment."
Genoa were forced to deny reports this week that their former player, Kakha Kaladze, was behind a consortium interested in purchasing the club.
Former defender Kaladze made over 50 appearances in Rossoblu colours but is currently working as Minister of Energy for the Georgian government.
Cristobal Jorquera is beginning his slow recuperation from a thigh strain, with fellow midfielder Marco Rossi and striker Marco Borriello not expected to resume training until next week at the earliest.