Celtic crashed out of Europe for the season after failing to break down AC Milan in their Champions League tie.
Shakhtar Donetsk's win over Barcelona meant that the Ukrainians pipped Celtic for the Uefa Cup spot in Group F.
John Hartson's first half shot was brilliantly saved by AC Milan goalkeeper Dida, while Celtic peppered the visiting goalmouth with crosses.
Serginho hit the woodwork for the visitors as the Italian side held out for a point to top the section.
Celtic started brightly and some neat footwork from Aiden McGeady saw him get beyond the AC Milan defence in the third minute but Chris Sutton could only glance the youngster's cross wide.
The lively McGeady then sent a 20-yard shot narrowly over the crossbar.
AC Milan rested some of their regular starters but could still call upon a glittering array of star names.
World Player of Year nominee Andriy Shevchenko showed his pace in the 12th minute to escape Bobo Balde.
The defender did well to recover and slide the ball away from the striker, and goalkeeper Magnus Hedman had to get down smartly to prevent an own goal.
Soon after, Shevchenko scorned a great chance when he completely missed the ball close the penalty spot.
Serginho smashed a thunderous strike against the crossbar from an acute angle and the same player shot wide a minute later as the Serie A side began to find their rhythm.
Celtic finished the first half strongly and visiting goalkeeper Dida made a wonderful save to push over Hartson's shot after a Jackie McNamara cross found the Welsh striker ten yards out.
Celtic couldn't put AC Milan under enough pressure
Balde then crashed into the penalty area and sent in a low cross that Dida flipped away from Sutton and McGeady's shot on the turn was charged down.
Five minutes into the second half, a rare slip from Paolo Maldini saw the ball arrive at Sutton's feet close to goal but the striker was taken by surprise and hooked it wide.
Dida then gathered a low shot from Sutton before he bravely cut out a Joos Valgaeren cross that the striker was chasing.
Celtic were seeing a lot of the ball but all too often their moves broke down near the AC Milan penalty box, with the visitors defending deep.
Dida was at full stretch to to tip away a low drive from McNamara but, hard as they worked, Celtic lacked the vital spark to break down the experienced Italian side.
Celtic: Hedman, McNamara, Balde, Varga, Valgaeren (Camara 66), Petrov (Juninho Paulista 76), Lennon, Thompson, McGeady, Sutton, Hartson.
Subs Not Used: Sylla, Laursen, Maloney, Wallace, Marshall.
Booked: Lennon, Camara.
AC Milan: Dida, Coloccini, Nesta, Maldini, Costacurta, Brocchi, Ambrosini, Dhorasoo (Kaka 86), Serginho, Rui Costa (Seedorf 80), Shevchenko (Crespo 63).
Subs Not Used: Fiori, Cafu, Gattuso, Pirlo.
Ref: Kyros Vassaras (Greece).