The Italian side host Tuesday's last-16 first leg against a Blues side at their lowest point of a stuttering season, the visitors having gone four games without a victory and winning just four of their last 13.
Chelsea would normally be favourites to progress against surprise packages Napoli, who are enjoying their first Champions League campaign.
But Mazzarri's team are being tipped to pile on the misery for their opponents, having already helped eliminate a markedly better side during the group stage in Premier League leaders Manchester City.
Mazzarri shunned the favourites' tag, saying: "Tomorrow, we will face a team, Chelsea, who have played more than 100 Champions League matches.
"We are proud to play this match but I don't want to hear anyone saying we are the favourite for this game.
"We can find a result only if we play a great match.
"All the team has to play not only a special game, but the perfect game."
A Napoli victory would do nothing to ease the pressure on Andre Villas-Boas, amid continued speculation over his future as Chelsea struggle to qualify for next season's competition.
Mazzarri, who will not pit his wits directly with his opposite number as he is banned for both legs, said: "I respect Mr Andre Villas-Boas, who is a really good coach.
"What Chelsea are doing in the Premier League is not important for this competition, because here we play only two matches and not a whole league and they have a lot of good players who can change the game in every moment."
Mazzarri warned his side against Chelsea's threat on the counter-attack, but he also promised the visitors a white-hot atmosphere at the Stadio San Paolo.
"Chelsea and Manchester City have a similar attitude - good games, good players and hard pressure," he said.
"We have to face them in the same way - with adrenaline and proud about our history.
"It will be important for us that Chelsea will not score any goals at the Stadio San Paolo.
"Tomorrow, the Stadio San Paolo will be amazing.
"When we play a match like this, we have the best supporters in Europe."
Mazzarri was banned from the tie for pushing Villarreal forward Nilmar during Napoli's final group game in December.
Assistant Nicolo Frustalupi will deputise, with the Italians having won all their previous games when he has done so.
Mazzarri said: "Nicolo Frustalupi is probably better than me as tactical coach and I'm sure that he will be a perfect coach tomorrow."
Napoli boast one of the most feared attacking trios in Europe in Edinson Cavani, Marek Hamsik and Ezequiel Lavezzi.
The latter is the only one of them yet to score in the Champions League - something he was planning to change tomorrow.
"I really hope so - it would be pretty nice to score my first Champions League goal against a team like Chelsea," he said.
"But I'm happy at the end of the game if I have helped the rest of the team to find the result - a good result."
He added: "This an important game but, if we are not quiet, we risk defeat.
"We are not the favourites, especially because Chelsea have much more experience than us.
"But I can assure you that we are hungry and we want to write an important page of our history."
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