Gigio Donnarumma saved a penalty before Krzysztof Piatek and Suso goals.
“It was a difficult game, we knew it would be and that Frosinone would come here with the right attitude. We had a scare, we thank Gianluigi Donnarumma for getting us out of trouble and can look to the next game," Gattuso told Sky Sport Italia.
“In my view, there has been a lot of chatter and I've been considered on the way out since pre-season. The table talks, look over the last six years at how many points Milan earned and look where we are now.
“I think we did what we had to do. Perhaps we fell away during the period where we had to finish the job and it dragged on longer than expected. We reached the Coppa Italia semi-final, went out in the first round of the Europa League.
“Those who need to judge me will judge me. I'll continue this work, I hope to do it at Milan, but either way I think I'm pretty decent and can keep learning. I can do better."