Lavezzi was sold to PSG last week.
Mazzarri said: "Lavezzi was an important player in my three years here. He has grown a lot and was sold for a substantial figure, he is a champion now set in stone.
"Last year we were very good as a group and Goran Pandev returned to a level we had not seen him at for a few seasons, when he had been under par.
"Now he has undisputed quality and I have a lot of expectations for this year for him as part of an attach with Cavani and Hamsik, who can give optimum guarantees.
"I expect a great deal from Pandev this year, he must reach his best and maintain it all year."