Patrick Cutrone and Hakan Calhanoglu were among the goalscorers.
“We all want the Coppa Italia, but we'll be up against a great side like Juventus," Gattuso told Mediaset Premium.
“They've got something more than us, but we're in good shape coming in to this match.
“Suso had a knock to the thigh, it was iced as a precaution when he came off. Today we saw the team playing with more freedom and it showed.
“Dropping points against the smaller sides is something Milan have struggled with a lot lately. It's an issue of mentality. Today we took our foot off the gas at the 70th minute and did everything to help Verona score."