Moratti attended the San Siro side's 2-2 draw with Napoli and remarked after the game that the 53-year-old's job could be in trouble if results don't pick up soon.
Mazzarri, though, insists he has no interest in what the 69-year-old has to say, instead turning his attention to Thursday's Europa League match with Saint-Etienne.
"I don't have time to think about what Moratti says, I don't even want to waste energy answering him," he told reporters. "I'm focused on St. Etienne. I just want my players to grow under my direction and make the most of it."
"It's a challenging game. We have studied our opponents and they are having a great championship in France, we respect them.
"Saint-Etienne is a team that has prestige, they are to be respected and that is doing well in their league, which is now very close to the Italian one.
"In tomorrow's game, everyone will have to play well to give continuity to what we showed against Napoli."
Mazzarri is without the quartet of Hugo Campagnaro, Danilo D'Ambrosio, Yuto Nagatomo and Pablo Daniel Osvaldo through injury for this game, meaning he has to make several changes for the French side's visit.
"We are in a total emergency in some positions and so it is not easy to play these games so close together.
"I will try to rotate the players based on who I have. I'll decide with the players themselves."
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