The Hoops were made to pay for missing several chances against the Serie A side, who went ahead through Kaka in the 13th minute when he headed a Valter Birsa corner past Fraser Forster.
Celtic defender Virgil van Dijk missed a sitter at the start of the second half when he blasted a shot straight at Milan goalkeeper Christian Abbiati - a minute before Rossoneri defender Cristian Zapata made it 2-0 from close range before Mario Balotelli added a third.
With Ajax beating Barcelona 2-1 at the Amsterdam ArenA, the Scottish champions remain bottom of the pool with three points ahead of their trip to the Nou Camp next month and do not even have the safety net of the Europa League this season.
Lennon said: "Tonight [Tuesday] 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.
"I think it's been 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.
"When our opportunities arose, Beram Kayal, Charlie Mulgrew, Van Dijk, James Forrest, snatched at them - that was the difference in the game.
"We have to improve if we are going to continue to play in the Champions League."
Asked if he felt a better quality of player was needed for the Champions League, the Northern Irishman replied: "I think that has been apparent over the course of the campaign.
"Realistically, getting into the Champions League was fantastic for us.
"When the draw was made, we knew how difficult it was going to be but we have competed - and we competed again tonight. But just that quality at the top end of the pitch has caught up with us, certainly this season anyway.
"Some of the players have covered themselves in glory, but it is mainly the defensive end of the pitch we are talking about.
"We all enjoy the European experience, but hopefully we can learn from this campaign and we will do everything we come back next year and compete in it again. That's the target now."
Forrest, who recovered from a hamstring strain to start the game, was arrested in connection with an alleged sexual assault in the build-up to the match, police said.
Asked if the player's off-field issues were a problem for him, the Hoops boss replied: "No it's not, no."
AC Milan arrived in Glasgow without a win in seven games and 13th in Serie A but were emphatic winners in the end, although coach Massimiliano Allegri admitted his side had to do some resolute defending.
He said: "It wasn't an easy win. Celtic played well but we were able to nullify them. They created three or four chances but we defended well.
"It is not about a turning point for us. We played well tonight, and were technically very good, but we have played well in other matches.
"We have to make sure we have a good Champions League campaign and, of course, we have to get back to form domestically.
"But it was a good result and a great performance."