The struggling home side got a huge slice of fortune when defender Cristian Zapata's drive in the 82nd minute appeared to be heading wide before it deflected off Parkhead left-back Emilio Izaguirre and ended up behind Fraser Forster.
The Hoops goalkeeper was beaten again four minutes later despite making a great save from Mario Balotelli's free-kick, as midfielder Sulley Muntari knocked in the rebound.
Lennon said: "I am bitterly disappointed because for long periods of the game we were the better team.
"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 next and they are a different animal. But we are here to qualify and nothing changes my view after that performance.
"We had really good chances tonight and that will be one regret going away from here."
Meanwhile, Lionel Messi scored a superb hat-trick as Barcelona ran Ajax ragged in their 4-0 win at the Nou Camp.
The Argentinian striker was at his effortless best, despatching a fine first-half free-kick and then producing two clinical finishes for a record four Champions League hat-tricks.
Ajax were passengers in the second period and were denied even a consolation when Victor Valdes saved Kolbeinn Sigthorsson's penalty.