Abbiati joined Milan from Monza in 1998, and ended his 18-year association with the club when he decided to retire at the conclusion of this season.
Milan endured another inconsistent campaign, Cristian Brocchi guiding the club to seventh following the sacking of Sinisa Mihajlovic in April.
The Coppa Italia failed to save their season as they lost to Juventus 1-0 after extra-time in Saturday's final, and Abbiati has subsequently been scathing of some of his colleagues for their conduct throughout 2015-16.
"There are four of five players that didn't do what was asked of them, and I'm not talking about making mistakes on the field," he told Gazzette dello Sport.
"The fact is that if it was just one player we could have isolated them, but because it was so many players, it was tough to do so.
"If I close my eyes and think back to the Milan sides I played for until 2011, I see a different team in every regard.
"I look at things by thinking about what Demetrio Albertini, Alessandro Costacurta and Paolo Maldini taught me.
"I've only been fined once in my career for arriving late. Whenever we lost, I never considered going out."