The Serie A side would have clinched progression had they emerged victorious at the Olympic Stadium but, although they threatened occasionally in the second period, their generally lacklustre display was hardly deserving of all three points.
AEK shaded a dour first half, creating a couple of half-chances to worry a Milan side who themselves looked utterly toothless in the final third.
Montella managed to get a little more out of his team after the break, though, with Riccardo Montolivo going close twice in quick succession – his second chance striking the post.
Milan improved considerably in the second half, moving the ball quicker and putting AEK's defence under pressure, yet they failed to enjoy a sustained period of dominance.
The latter stages became somewhat more frantic, but neither side looked to play with any more conviction than before and it remained goalless, leaving Group D leaders Milan - who have just a single win in their last seven matches across all competitions - on eight points, two clear of second-placed AEK.
Milan showed little sign of putting their domestic woes behind them during the early exchanges, with AEK looking significantly more purposeful.
Rodrigo Galo was the first to go close for the hosts 11 minutes in, seeing his dipping 25-yard volley go agonisingly wide of the bottom-left corner.
Gianluigi Donnarumma was then called into action a few moments later, denying the tricky Sergio Araujo at the near post after a Fabio Borini error invited pressure and the hosts finished the half on top as Galo went close again, his curling left-footed effort from the right flank flying just past the top-left corner.
Milan went into the half-time break having failed to touch the ball in AEK's penalty area, highlighting their poor showing.
Montella introduced Suso for the disappointing Patrick Cutrone for the second half and Milan suddenly appeared more urgent and calculated in possession.
Suso almost set Montolivo up for the opener nine minutes after the break, with Giannis Anestis blocking the Italy international's close-range effort after Suso's clever ball in from the right.
Montolivo then went even closer a couple of minutes later, shooting against the left-hand post after being released into the area by Hakan Calhanoglu.
Milan enjoyed some late pressure, though the closest they went to a goal was Ognjen Vranjes's awkward clearance over his own goal from close range after a Suso cross, with the match ultimately petering out into the kind of drab encounter that will do little for Montella's job prospects.
Key Opta stats:
- AC Milan have failed to win each of the last three European match against AEK Athens (D2 L1).
- AC Milan have kept a clean sheet in six of their eight European games this season.
- Only against Sampdoria (0) have AC Milan fired less shots on target in a game than today (two) in the current season.
- Only one shot was attempted by AC Milan in the first half (Leonardo Bonucci at minute 44) - the lowest total in a game by Milan this season.
- Leonardo Bonucci made the most touches (111), passes (101) and completed passes (84) in this match.