The Scottish champions were looking to spring a surprise and put the Italians, who started as favourites, to the sword on home turf.
Celtic began well, but AC Milan took what chances came their way and went 1-0 up in just the 14th minute through Rade Krunic.
Brahim Diaz made sure that the visitors would go in 2-0 up at the break when he netted in the 42nd minute.
Celtic changed their shape in the second half and pushed AC Milan, pulling a goal back 14 minutes from time through a Mohamed Elyounoussi header.
However, AC Milan held off the hosts and grabbed a third in stoppage time through Jens Petter Hauge.
Christie was brought on at half time by Neil Lennon and the Celtic attacker admits he is gutted to have finished on the losing side.
“I’m gutted to lose tonight”, he told Celtic’s media.
“I did feel like we could have pushed forward and got an equaliser but there’s positives to take from the second half”, Christie added.
The other game in Celtic’s Europa League group saw Lille visit Sparta Prague and run out 4-1 winners.