Javier Hernandez scored twice in the second leg to send United through 2-1 on aggregate with Wes Brown's own goal on 82 minutes coming too late to inspire a full Marseille comeback.
France's L'Equipe newspaper labelled the defeat "the Theatre of Regrets" in reference to Old Trafford's nickname of the Theatre of Dreams and Marseille's feelings of frustration after a dour 0-0 draw in the first leg at the Stade Velodrome.
"We are disappointed, we were not so far away from a great result but it's now necessary to move forward and quickly," midfielder Stephane Mbia told reporters.
"There are lots of regrets for us but you've got to recognise that Manchester United did a good job."
The French champions had decent pressure after the interval but could not sufficiently break down a United defence shorn of injured captain Nemanja Vidic and Rio Ferdinand.
Didier Deschamps' men, who lie fourth in a tight French top-flight, will now return to domestic action trying to sew up a second straight Ligue 1 title despite their European disappointment.
"We had the opportunity to do something better. We had chances," the coach ruefully remarked.
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