A 1-0 home loss to Atalanta left Milan six points off the Serie A summit at the weekend and they were desperately hoping a European night could get their campaign going on Tuesday.
But instead they looked tentative and allowed Anderlecht the better of the chances on the night in the Group C clash at the San Siro.
The visitors started the brighter, with Bram Nuytinck having a powerful shot charged down before a fine effort from Sacha Kljestan was parried away by Christian Abbiati.
Milan began to probe, earning a corner from which Kevin-Prince Boateng headed wide, while efforts from further afield by Mattia De Sciglio and Mathieu Flamini were dealt with by the Anderlecht defence.
Anderlecht were still enjoying plenty of the ball against their nervy hosts and Kanu, Dieumerci Mbokani and Guillaume Gillet all had further efforts blocked, the latter by another good save from Abbiati.
Nuytinck fired wide from a corner as Anderlecht kept Milan on the back foot.
Boateng was looking like the sharpest of Milan's players going forward. He headed wide from another corner but then brought a save out of Silvio Proto with a close-range volley.
Moments later, Urby Emanuelson tested the goalkeeper with an even better effort.
But it was not the start of any great period of Milan domination and they were again on the back foot before the break, with Massimo Bruno, Mbokani and Cheikhou Kouyate having chances for the visitors.
Anderlecht had their best chance to take the lead early in the second half.
Lucas Biglia, who had moments earlier seen a long-range effort blocked by Daniele Bonera, got into a great position only to slice wide on the volley.
Milan responded with Emanuelson flashing a shot wide before Boateng sent yet another header wide, this time from a free-kick.
Antonio Nocerino then stretched Proto with a shot across goal before Stephan El Shaarawi's header brought an excellent save from the Anderlecht goalkeeper.
Milan were in the ascendancy now, but could not do anything to make it count.
Emanuelson blazed over, Flamini headed wide, and El Shaarawi's effort was tame.
A powerful free-kick from Kevin Constant was straight at the wall.
Instead it was Anderlecht who had the final chance to win it, only for Mbokani to send his strike from the edge of the area over the crossbar.