"Milan took their chances, but we contributed to our downfall. We have to improve if we are to continue to play in the Champions League," Lennon told reporters.
"We all enjoy the Euro experience but we'll learn from this campaign and we will do everything we can to come back next year and compete."
However, despite that, Lennon added that he didn't think his players were outplayed by the Italians and urged them to turn their attention to Sunday's match against Hearts.
"I didn't think we were outplayed, it wasn't wave after wave of attack. We have a big game Sunday. We have players here who need more game time to prove themselves and bed themselves into the squad," he continued.
Celtic's last match in Group H is against Barcelona.