The Partenopei were trailing 2-0, but completed the comeback to win 3-2 in under 30 minutes with a Piotr Zielinski brace and Dries Mertens off the bench.
“The biggest regret is that after the goal for 2-1, we simply disappeared from the game," Gattuso told DAZN.
“Everyone started interpreting the match in their own way and we got lost. We've got to figure out how to improve this aspect of the side and I was disappointed by the lack of reaction we showed.
“I take full responsibility, because if the team is afraid, then that is the fault of the Coach. We just switched off after the first mistake and it happened many times last season."
Lucas Biglia was caught in possession for the goal that re-opened the match, although the Milan Coach saw it differently.
“It was Mateo Musacchio's error, he can't pass it like that, but I don't like talking about individual mistakes. We dominated for 55 minutes, but at the first distraction we just collapsed and allowed Napoli back into the game.
“After their goal, we didn't play as a unit anymore. It hurts me to play so well at the San Paolo and then emerge empty-handed. Now we have to lick our wounds and go forward."