The Serie A side scored twice in the final 10 minutes through an Emilio Izaguirre own goal and Sulley Muntari - as the Scottish outfit produced a fine display at San Siro
The Scottish champions were undone in the last 10 minutes by an Emilio Izaguirre own goal and a close-range Sulley Muntari effort at San Siro in their Group H opener.
However, Lennon was pleased with his side's performance and felt that they deserved more from the game.
"We dominated the game for long periods," Lennon told reporters.
"I said to the players that when you are on top you need to take your chances. I thought we were brilliant. Sometimes in football you don’t get what you deserve. I couldn't see Milan scoring in the second half."
Celtic captain Scott Brown also lamented Milan's "lucky break", adding that he is targeting revenge in the reverse fixture in November.
"We played really well. We created a lot of chances and I think overall we were probably the better team," he said.
"They got a lucky break. We know we are a good team and there is always the rematch."