The Nerazzurri boss does not expect trouble from the San Paolo crowd after leaving the club over the summer.
The 52-year-old coached the Partenopei from 2009 until the end of last season, when he decided against extending his contract to take charge at San Siro.
But despite being criticised for his decision to walk out on the club by Napoli president Aurelio De Laurentiis, Mazzarri believes the supporters should remember the good times they shared together.
"I spent four unforgettable years there. Wonderful years but now I'm thinking about preparing my players, making sure they know what could happen tomorrow," he told reporters. "I think that intelligent, level-headed people are capable of recognising people's merits and faults.
"At all the clubs where I've worked the fans have appreciated me. Fans have to respect what a person decides to do at the end of a contract."
Inter heads into the fixture on the back of three consecutive Serie A draws, but Mazzarri insists his men are still exceeding all expectations.
"We're doing better than the best expectations. We've dropped points along the way but generally speaking we're doing very well," he continued. "The game will be played in a stadium where the fans have been able to make the difference in the past. I've tried to explain to my players what sort of atmosphere to expect.
"What I say to my players is that we must never be satisfied and always try to go as high as possible, but let's not forget where we started too. Other prestigious clubs have had to start over again at times."
The Nerazzurri presently lie fourth in Serie A, four points behind Sunday's opponents Napoli, which sits in third.