The Dutch side were eliminated from the competition following the stalemate, but their coach insists that their opponents adopted "anti-football" tactics to see out the game.
"UEFA always talks about respect, but if even the ballboys don't provide us the balls if we're in a hurry. They stalled the match for 20 minutes, but there was only five minutes extra-time. It's a disgrace," he told NOS.
Milan were reduced to 10 men when Riccardo Montolivo was shown a straight red card, and De Boer believes that his side went on to dominate the game.
"It was rather difficult after the red card. We had to search how to play. We needed a bit of luck, but we didn't get it. We had some chances, but unfortunately anti-football won today," he said.
"Milan played their game with 10 men with their back against their own box. I'm proud of the boys and how they fought. It just felt like we played in a theatre tonight, what with all these tricks of Milan's.
He added: "At these moments, the ref let the game slip out of his hands. The Milan goalkeeper took a minute for every goal kick. We were twice as good as Milan. It's something positive, but at this point it's disappointing."
Ajax finished in third place in Group H, which sees them drop into the Europa League.