It was the second successive defeat after the Old Firm defeat by Rangers at the weekend but the Celtic boss looked for positives.

"I'm disappointed we lost," said Lennon.

"I thought we deserved something from the game. We were very good in the second half, a lot better, better play, better body language but we lacked a cutting edge.

"We got into good areas in the first half but the final ball needs to be better at this level, we gave away two soft goals.

"But we made changes at half-time and we played better in the second half.

"It was markedly better than the weekend. It was encouraging. I don't like losing but there were a lot of good signs for me.

"I wanted an improvement and we got a big improvement. Part of me is quite pleased with that.

"We could have shied away from it all after the criticism we have taken and I have taken but they showed their personality in the second half."

Lennon admitted he was concerned about the goals his side conceded.

The former Celtic captain said: "Yes, the two goals are definitely avoidable, especially the first one.

"It was the Milan's first real attack, we had started on the front foot and we have to be far tighter and secure. It was disappointing.

A header in our box, eight yards out and we had enough bodies back to deal with the counter attack at the second goal.

"The reaction was very good, there was real belief about them in the second half.

"It gives us a lot to think about going forward now and we are getting players back.

"That was a good test against a good side and we coped with it very well in the main.

"I am bitterly disappointed to have lost at home again."