CSKA Moscow were unable to pull off a shock win over PSV Eindhoven, and United now face the prospect of playing Europa League football in the new year.
Manager Louis van Gaal wanted to guide United to Champions League glory, but he will have to get used to long trips to far-flung corners of Europe on Thursday nights instead.
United may have been beset by injuries, but Van Gaal cannot use that as an excuse. United should have cruised through this group and the Dutchman's critics will now only grow louder.
Without seven first-team regulars, Van Gaal was forced to hand defender Guillermo Varela his full debut. The Wolfsburg fans did their best to try to make David Moyes' first signing feel uncomfortable and so did the players tearing about the pitch in white and green.
The hosts lived up to their nickname of Die Wolfe and hounded United like a pack of aggressive wolves.
Van Gaal's team were never allowed to settle on the ball. Varela drifted inside, allowing Andre Schurrle a chance to shoot but he fluffed his lines and United breathed again.
Wolfsburg were well on top but somehow found themselves behind in the 10th minute.
Daley Blind found Juan Mata, who carved open the Wolfsburg back four to set Martial free. The Frenchman went into the game in poor form, but his finish was exemplary. He took one touch before rolling the ball past Diego Benaglio.
It was a superb finish, but Wolfsburg equalised with an even better one just three minutes later. Ricardo Rodriguez whipped in a low cross and Naldo got in front of Chris Smalling before volleying past David De Gea. United were back to square one.
Fellaini almost put them ahead again with a close-range header but Benaglio saved. Wolfsburg went on the attack at a devastating cost for United.
Wolfsburg switched the play from right to left and Schurrle drifted infield before laying the ball off to the sensational Julian Draxler. He glided past Bastian Schweinsteiger and two more United players while playing a one-two with Max Kruse before squaring to Vierinha, who slotted the ball in from close range. It was a stunning goal, one worthy of a team seemingly bound for a place among Europe's elite.
Draxler drew yet more gasps from the despairing United fans when he wriggled free in the box, but De Gea saved his shot.
United were reeling. They needed the half-time whistle to regroup. Instead they were handed another problem as Darmian had to be replaced by 19-year-old Cameron Borthwick-Jackson because of an injury to the Italian.
United thought they had equalised when Jesse Lingard's ball sailed into the goal, but the referee ruled Mata, who was in an offside position, had interfered with play.
United performed better at the start of the second period. Memphis Depay drew a save from Benaglio with an acrobatic volley. Wolfsburg still looked dangerous though. De Gea tipped an effort over from Schurrle and Kruse missed a sitter.
Van Gaal threw on Nick Powell for his first game in almost a year.
United supporters' spirits were raised when CSKA took the lead, but PSV soon equalised and Van Gaal's men were heading out. They needed an equaliser and they got it when Guilavogui knocked Fellaini's header into his own net, but just a minute later Naldo headed in to send the locals inside the Volkswagen Arena wild.
United pushed for an equaliser but it did not come. It would not have mattered anyway. PSV's winner in Eindhoven meant United were already out.