Both sides started cautiously which left an impatient AC Milan support baying for more action. Gradually their side began to look comfortable on the ball and created more chances in the first half without ever really troubling Artur Boruc in the Celtic goal.
At the other end Aiden McGeady showed flashes of brilliance on the break but, on a bare and patchy pitch, the visitors were easily dispossessed.
Filippo Inzaghi, who started the match just one goal off the record for leading scorer in European competition, looked dangerous as he tried to get on the end of every ball to add to his tally.
He, along with Massimo Ambrosini and Kaka sent in early shots which were all off-target. Eventually Inzaghi found the target but Boruc was more than capable of gathering his effort which lacked power.
Milan were forced to make an early defensive reshuffle when Dario Simic was forced off the pitch with injury bringing on Georgia international Kakha Kaladze in his place.
The change didn't do their back line any harm though as they continued to dominate the Celtic attack. The Bhoys' only real chance of the first half came from defender Jiri Jarosik whose effort was easily saved by Zeljko Kalac.
Scott Brown started the half badly as he picked up a yellow card which will keep him out of the first game of the next round.
But he nearly made up for it minutes later beating Kaladze and making a brilliant run on goal but mis-hitting his shot completely.
AC Milan looked more determined in front of goal than they had in the first half. Clarence Seedorf had his attempt blocked by a diving Gary Caldwell and shortly after Inzaghi sent a header straight at Boruc.
But they eventually made the breakthrough on 70 minutes as Kaka linked up with veteran Cafu whose cross was met by Inzaghi just inside the six-yard box and turned into the net.
Unwilling to rely on the result in the Ukraine, Celtic battled to try and get the point they needed.
McGeady came close with a well-taken free-kick which was saved by Kalac. But Milan still looked the more likely to score with Kaka beating everyone including Boruc before narrowly missing an empty net.