Emilio Izaguirre's own goal and a Sulley Muntari strike in the final 10 minutes secured a 2-0 win for unconvincing AC Milan over plucky Celtic in their Champions League Group H opener on Wednesday.
A raft of injuries to key Milan players including Kaka and captain Riccardo Montolivo forced coach Massimiliano Allegri to reshuffle his squad and gave Neil Lennon's men hopes of causing a major upset at the San Siro.
But after a promising second half from the visitors, in which striker Anthony Stokes hit the woodwork with a curling free kick, Izaguirre's unfortunate own goal from a wayward Cristian Zapata strike broke the deadlock on 82 minutes and Muntari poked home a rebound from Mario Balotelli's free kick three minutes later.
It was an agonising finale to a second half in which Celtic dictated play for long spells, and Lennon could not hide his disappointment.
"We're bitterly disappointed," said the Northern Irishman. "We dominated Milan from about 20 minutes on in the first half until around 10 minutes to go in the second half.
"We frustrated them and we played really good football. We had good chances tonight but you have to take your chances.
"I think the scoreline flatters Milan tonight."
Allegri conceded it was a flawed performance but while he admitted some luck had gone Milan's way he insisted the Rossoneri played as well as they could given the absence of two key defenders as well as Brazilian playmaker Kaka and midfielder Montolivo.
"We faced certain challenges due to missing personnel and players playing in positions they were not used to," said Allegri.
"We also came up against a strong team with strong players. We might have been a little lucky but overall the team played solidly tonight."
Having battled through a tough qualifying campaign, Celtic came to Milan brimming with confidence but with 20 defeats in their previous 22 away games in the competition, history was against them.
And after just four minutes Balotelli forced a good block from Fraser Forster after volleying Valter Birsa's delivery from 12 yards out.
A Balotelli headed flick-on was then blocked by Forster and unmarked Antonio Nocerino saw his dipping half-volley from Phillipe Mexes's cross sail just over.
Celtic began to grow in confidence near the end of the half but Stokes spurned a chance when he sent his angled shot into the side-netting after turning Kevin Constant.
Milan, meanwhile, finished the half as they had started, Balotelli collecting Alessandro Matri's lay-off and seeing his deflected low drive force Forster to parry while Muntari half-volleyed a poor clearance barely a metre over.
Milan kicked off the second half and while Celtic moved up a gear, Lennon's men were denied at every opportunity.
Kris Commons, Mikael Lustig and Georgios Samaras came close for Celtic, and although Milan briefly threatened on the hour the visitors came fighting back again.
After a Balotelli free kick hit the defensive wall, Celtic countered to give Scott Brown a solid scoring chance, but the skipper's tame shot was collected by goalkeeper Christian Abbiati.
Celtic came agonisingly close when Stokes sent in a delightful free kick from 25 yards clattering into the crossbar.
It was a miss that would prove costly minutes later when Zapata hit a low drive from 20 yards out which was heading well wide until Izaguirre stuck out a foot and diverted it inside the post, with Forster rooted to the spot.
Milan grabbed their second five minutes later when Balotelli's powerful free kick was somehow kept out by the keeper, only for Muntari to pounce from close range to fire home the rebound.