Napoli are third in Group A with five points from four games and a home victory over Manchester City on Tuesday would move them into second and leave them poised to qualify for the last 16.
"When the group was drawn, I believe it was unthinkable that we would get to the fifth round of matches with still a good chance of qualifying," Mazzarri told reporters.
"To be playing for a place against Manchester City gives us great satisfaction and I think is somewhat unexpected."
"It means that we have done something extraordinary. Anything that comes after this will be like gold."
Bayern Munich, seen as clear favourites to go through with big-spending City when the group was drawn, lead and Spain's Villarreal prop up the standings.
Striker Edinson Cavani, whose 26 Serie A goals propelled Napoli to third place last season, shrugged off concerns about his relative lack of scoring this term.
"I just hope to give some excitement to our supporters and to do well for Napoli," said the Uruguayan.
"I'm happy and feel I have the support of the coach. I know the he likes the way I work, the way I move on the pitch and the goal is a matter of time."
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