Cristian Zapata's shot deflected off the right boot of Emilio Izaguirre to put Milan ahead late on, before Sulley Muntari scored a second just five minutes from time. The goal had come after Fraser Forster, the Celtic goalkeeper, had parried a free-kick from Mario Balotelli.
Lennon did not consider the scoreline to offer a true reflection of the match and instead was heartened with the performance of his own side. The Celtic manager is convinced that the efforts of his players have proved that they will be able to compete to progress to the next stage of the competition this season.
"I am bitterly disappointed because for long periods of the game we were the better team," said Lennon. "To come away from the San Siro, [disappointed] not to have picked up a point or three points, is a mark of how well we have developed and how well we played tonight.
"We have Barcelona [at home] next and they are a different animal. But we are here to qualify and nothing changes my view after that performance. The scoreline flattered Milan, I don't think there was two goals between the teams. We dominated from 20 minutes on in the first half, until 10 minutes from the end of second. Apart from the Muntari chance, my goalkeeper had nothing to do the second half, we restricted them to long-range shots and we played really good football. There were no failures."
He included Anthony Stokes in that assessment. The striker was given the task of leading the line for Celtic in Europe and he came close to marking that rare responsibility with a goal - his free-kick in the second half hitting the crossbar.
"We played really well and created a lot of chances," added Scott Brown, the Celtic captain. "Overall I felt we were probably the better team. They got the lucky break and we were always going to try and push forward [and that allowed them to get the second goal].
"Was I surprised by how much possession we had in the game? Not in the slightest. We knew we were going to get possession. We know we are a good team. We gave just as good as we got."
Nigel de Jong, the Milan midfielder, was in agreement. "We let Celtic dictate in the first half. Celtic were, mentally, a lot stronger."