The Hoops required a win to keep their hopes of qualifying for the Round of 16 alive and at least a draw to be in the running for a third-placed finish but could not muster either as they remained bottom of Group H after Ajax shocked Barcelona in Amsterdam.
Kaka, Cristian Zapata and Mario Balotelli scored for the Rossoneri but at 1-0, Virgil van Dijk missed a great chance to level for the home side which manager Neil Lennon felt could have turned the game completely.
"Tonight was symptomatic of the campaign. We missed good chances and I was really disappointed in the two goals we lost from corners because we take a lot of pride in that," he said.
"I think it some time for a long time that someone scored from a corner.
"The Virgil chance was a great chance, and at 1-1 the game could have gone either way. And then we go and concede again from a corner. That was the most disappointing aspect - as was the opportunities we have missed.
"I didn't think we were outplayed or there were waves after waves of attack.
"But big moments change the psychology of the game. Milan took their chances when they came along, albeit we contributed to our own downfall.
"We have to improve if we are going to continue to play in the Champions League."
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