Dennis Man had Parma ahead after two minutes, Christian Pulisic found AC Milan's equaliser after 66 minutes, before Parma's winner came from Matteo Cancellieri.
Fonseca was unimpressed by Milan's defending, stating afterwards: “I have to say, the main responsibility for what happens with this team lies with me.
“I take responsibility and I don’t want to hide away from that. However, it’s clear to me that there is a collective problem when it comes to defending and aggression.”
Asked about his players' attitude, Fonseca replied: “I think it’s everything. This team has a problem generally. We had problems when we didn’t press too high against Torino. Today we tried to get players to press higher, and we still had problems.
“When someone played through our pressure, it became difficult to stay compact and recover our positions. When we got back into position, we were passive. There are lots of things. To me, it’s a problem with attitude, energy and desire to defend as a team.
"The truth is that we had a good pre-season, but this here is our reality. It is always easier to play against big teams, you are more motivated.
“We came here and there was a change that is really difficult to understand. During the week, when we prepare our strategies, the team does really well. Then it gets to the game and we start acting like this, it’s difficult to explain.”