The coach was furious with the hosts' time-wasting tactics, but praised his team for playing "twice as good" as the Rossoneri despite being knocked out of the Champions League
Riccardo Montolivo was sent off for a terrible challenge on Christian Poulsen midway through the first half at San Siro but a valiant defensive effort saw the Rossoneri clinch second spot in Group H and scrape through to the last-16.
De Boer told NOS: "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.
"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.
"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.
"It's experienced by Milan, but the ref allowed it. The fact that he gave red had nothing to do with it. A red card is a red card. [Mario] Balotelli should have gotten red as well after he kicked Daley Blind. He didn't have any intention to play the ball.
"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 dissapointing."
Ajax's third-place finish in Group H sees them drop into the Europa League.