The off-form Scottish champions had already been knocked out of the Europa League by the time they travelled to the San Siro, but they stunned the Serie A leaders with early goals from Tom Rogic and Odsonne Edouard and could have added to that lead.
Jens Petter Hauge scored a fine third five minutes after the break and, in the 82nd minute, Milan substitute Brahim Diaz added a fourth to leave the Parkhead side with one point from five Group H games and two wins in their last 11 matches in all competitions.
Hoops boss Lennon, however, insisted there were plenty of positives to be taken as he turns his attention to the Premiership clash against St Johnstone at home on Sunday.
He said: "We took the game to Milan. We tried to get a bit of respectability back to our performance and I felt we got all that.
"We looked far more like ourselves and I think the scoreline didn't do us justice.
"But I think there is a lot to be positive (about) now going forward. The players at times showed what they're really capable of.
"I don't think I've ever been involved with a team that's gone 2-0 up in the San Siro, regardless of the circumstances.
"We created quality chances and they had to rely on their goalkeeper to keep them in the game.
"I'm sitting here disappointed, obviously, as it's another defeat and it's a sore one to take.
"But I'm also very proud of the reaction and their will to put on a performance. We looked far more like a Celtic team that I know.
"The players are disappointed because they felt they were always in the game. They are really good professionals who like to win.
"We're talking about playing AC Milan in the San Siro and we're sitting here disappointed that we haven't got something out of the game.
"We must take something from it. People may say it's another defeat and another four goals. I get that and I understand it. But the quality of opposition was top class.
"And the performance from our team and as individuals was a very, very high standard."