Under-fire Neil Lennon insists he saw signs of the real Celtic again and they won back respectability in the San Siro.
But the Parkhead boss admits his team still need to toughen up and be more streetwise if they are to find the solidity to really get themselves back to their best levels.
And he admits there may be a mindset issue to iron out in an attempt to stop the leaking of bad goals.
Lennon was hugely heartened by aspects of the display during the 4-2 defeat.
Celtic were two-up through Tom Rogic and Odsonne Edouard and had other chances in an offensive show that pleased the manager.
But Lennon was left dismayed at a lack of calm that allowed Milan to level before the interval and then a physical weakness in the defending which allowed the Italians to win it as Celtic took their goals against tally to a shocking 17.
He said: “We looked far more like a Celtic team that I know.
“I was delighted in a lot of aspects of our play. I thought we looked a real threat.
“We’d a chance to go 3-0 up and we were rampant at that stage. It’s a bit of quality at their first goal and a bit of nativity at their second.
“It was our free kick, it’s 2-1, we just need to settle and we take it quickly. It’s game management, really.
“We needed to take the sting out of it and slow it down a little bit, but because we were in a positive frame of mind we took a quick one and lost the ball.
“The third and fourth goals from our point of view are poor.
“We’ve let ourselves down not being physical enough in the tackle.
“It’s not as if we were cut open. We’d plenty of players back to deal with it but we don’t.”
Asked if that was as much about mindset as actions, he continued: “It may be as they’ve conceded a lot of goals in this group.
“If that’s the case we have to work on that.
“Is it naivety? Maybe. We just have to be a little bit smarter in those situations.
“I thought actually that we had probably more shots at goals and worked the goalkeeper more than they did to us.
“Even at 3-2, I thought we were always in the game and (Gianluigi) Donnarumma made a great save from Ryan Christie's free-kick and we looked a threat all night.
“I’ve got to take the positives from that. From the way we played, the way we passed the ball, the way we created chances.
“We took the game to Milan. I wanted us to get a bit of respectability back to our performance and I felt we got that.
“We looked far more like ourselves and I didn’t think the scoreline did us justice. There is a lot to be positive now going forward.
“The players at times showed what they’re really capable of. We looked a good team. The body language was good, the attitude was good.
“The scoreline doesn’t do us justice, but I’ve got to be happy with a large parts of the game.
“We scored two really good goals and had really good chances to win.”
Keeper Vasilis Barkas was guilty of poor positioning as Milan got back into the game with a Hakan Calhanoglu free-kick.
But Lennon refused to point any fingers and said: “I’m not going to single out individuals. We’ll analyse it as a group and take it forward from there.
“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.
“I’m disappointed as it’s another defeat and it’s a sore one to take. But I’m also very proud of their will to put on a performance.
“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, very high standard.”