UEFA Champions League: A seventh successive away defeat on Champions League duty meant Celtic's hopes of life beyond the initial group stage are looking grim as Filippo Inzaghi and Andrea Pirlo struck with late goals after a Stanislav Varga equaliser had offered brief respite.
After defeat to Barcelona in their opening game, the Scottish champions look down and out ahead of the double-header with Shakhtar Donetsk.
The game had barely begun before David Marshall was called to arms, Celtic's goalkeeper doing well to turn Kaka's shot round a post. Deployed in the hole behind Andriy Shevchenko and Jon Dahl Tomasson, Kaka continued to ruffle Celtic's back four and swiftly created an early goal for the Ukrainian.
Having drifted out to the right, the Brazilian began honing in on the penalty area, riding a series of tackles - one by a desperately backpedalling Chris Sutton - before squaring to Shevchenko whose crisp, first-time, left-foot shot did the rest after an untended late burst into the box.
If Varga's role in that slapdash slice of marking served as a reminder of just why the Slovakian could not command a place in a struggling Sunderland side, none of O'Neill's back line looked assured.
Celtic again had Marshall to thank for a wonderful one-handed save from the increasingly impressive Kaka, but Henri Camara wasted a rare chance, scooping his shot over.
Neil Lennon failed to exert any sort of control over a tempo largely dictated by Pirlo, and Alan Thompson struggled to get past the supposedly suspect Cafu, some of Milan's off-ball movement was exemplary.
One dash by Tomasson set up Shevchenko for a shot which almost resulted in an own-goal on Bobo Balde's part. With the need to equalise now imperative, Celtic too often resorted to highly speculative punts in John Hartson's direction.
Unfortunately, when Sutton ghosted out wide to the right and supplied Camara with an inviting, intelligent low cross, the striker seemed to get his feet tangled and totally miskicked.
Manager Martin O'Neill would have been relieved to get his players in at the break with just one goal between the sides.
Celtic had re-emerged with three at the back and Didier Agathe pushed forward into midfield. It appeared to be working as they enjoyed their first patch of sustained attacking pressure but fortune frowned when Thompson pulled up with a hamstring injury, giving way to Juninho.
Varga did make amends for his earlier oversight by equalising when left unguarded long enough to power in a header from eight yards. He became the first man in a Scottish side to score against AC Milan in the San Siro.
But in the dying minutes the substitute Inzaghi and Pirlo struck to send Celtic home empty-handed again.
Afterwards O'Neill claimed he was more upset by last night's defeat than after their UEFA Cup final loss.
O'Neill was inconsolable after the way his players lost their second Group F game in such similar circumstances to their first, against Barcelona.
"I feel terrible," said O'Neill. "I thought that losing (to Porto) in Seville (in the UEFA Cup final) was a really big disappointment - I know that was a couple of years ago now.
"Tonight I thought that in the first half we were tentative - but we were absolutely fantastic in the second half. When we came to grips with the game we stormed back and we dominated proceedings in the San Siro.
"I have massive disappointment but I am really proud of the team. I am disappointed only for the team."
O'Neill was gratified that at least Celtic gave their travelling support some reason to cheer along the way.
"The supporters have been fantastic, and it was a great evening for them to come and support the team. It was an incredible effort. But the players are absolutely despondent, and eventually this is a results business. We have been beaten in a game we dominated."
AC MILAN: Dida, Cafu, Nesta, Maldini, Pancaro, Gattuso (Rui Costa 86), Pirlo, Seedorf (Ambrosini 77), Kaka, Shevchenko, Tomasson (Inzaghi 77). Subs Not Used: Fiori, Kaladze, Costacurta, Crespo. Goals: Shevchenko 8, Inzaghi 89, Pirlo 90.
CELTIC: Marshall, Agathe, Varga, Balde, Valgaeren, Petrov, Lennon, Sutton, Thompson (Juninho Paulista 59), Hartson (Sylla 86), Camara. Subs Not Used: Douglas, Lambert, Laursen, Wallace, McGeady. Booked: Sutton. Goals: Varga 74.
Referee: G Veissiere (France).
Guardian Service