The Serie A outfit are a point above Didier Deschamps' team in Group C and a win at FC Zurich next month would put them through, leaving Marseille needing to beat leaders Real Madrid 4-0 in southern France to steal the other qualification spot.
"The result is not so good, sure a draw in Milan means something but we've hit the post and the bar," Deschamps, whose side lost 3-0 in Madrid in September, told a news conference.
"We've got to dream and hope but winning 4-0 against Madrid is not a small thing."
The lead did not last long however, with Milan's defence looking as shaky as Marseille's backline.
The French side's captain Mamadou Niang cruised past fullback Massimo Oddo on 16 minutes and his cross was palmed by Dida straight to Lucho Gonzalez, who could not miss from 10 metres out.
TIRED BADLY
Marseille had the better of the second half with forward Brandao spurning the best chance when he clipped the bar from close in after Niang's cross.
"Unfortunately we don't have all the players available. We had a balance...and changes could have caused problems," said the Brazilian coach, whose team won in Marseille in their opener but have not been victorious at home in the group.
"In Zurich we've got to be very concentrated on our game. The important thing is that it depends on us, a good result and we qualify."
The home side did come close through Borriello's header in the closing stages and had earlier been denied a penalty when Gianluca Zambrotta was booked for diving in the box after nice work by Ronaldinho.
