The Hoops dominated possession for large parts of the game but were unable to take advantage, with Anthony Stokes' second-half free-kick which clipped the crossbar the nearest they came to finding the net.
An 82nd-minute own goal from Emilio Izaguirre and a Sulley Muntari (85) effort from close range secured the points for Milan, but Lennon bemoaned the numerous opportunities the Scottish champions passed up.
"We dominated the game for long periods and I just said to the players in there, 'When you're on top, you've got to take your chances'," he told Sky Sports.
"Anything can happen - a ricochet or deflection and that's what happened. They didn't deserve it but sometimes you don't get what you deserve in football.
"I thought we were brilliant. I thought we started off a little bit nervous but after about 15, 20 minutes we took the game to them.
"Certainly in the second half, I couldn't see Milan scoring early - the goalie had nothing to do.
"I didn't see the incident for the free-kick for the second goal so I can't really comment on that, but we played very well and it's very disappointing to come away with nothing."
Next up for Celtic is a home game against Barcelona on October 1 and Lennon is expecting a much sterner test than his side experienced in Milan.
"Barcelona's a different game, a different animal," he said.
"I felt confident with the team coming into the game tonight and we did very, very well but not well enough for my liking."