United were already assured of top spot in the group and a place in the last 16 while Young Boys finished bottom and were eliminated.
With little at stake, interim United manager Ralf Rangnick made 11 changes from the team which beat Crystal Palace on Sunday and if it was a chance for some of those left out of recent line-ups to stake their claim, few would have impressed.
Rangnick's preference for high-intensity pressing football had been evident in the win over Palace but this, perhaps understandably given the unfamiliar selection, was a ramshackle display.
One of those who did make a case for a starting place was Mason Greenwood and it was the forward who gave United the ideal start, producing a super volley from a Luke Shaw cross to put the home side ahead in the ninth minute.
United were sloppy, though, and conceded several openings for David Wagner's Swiss side who drew level three minutes before the interval.
United's Dutch midfielder Donny van de Beek, one of those who need to impress, poorly gave away the ball on the edge of his own box and Fabian Rieder curled it into the corner.
United struggled to find any fluency after the break and Young Boys wasted several chance to win the game, most noticeably when Quentin Maceiras was found in space on the penalty spot but poked his shot wide.
Rangnick, who had handed starts to youngsters Amad Diallo and Anthony Elanga, introduced four academy products after the break included Charlie Savage, the 18-year old son of former Leicester City and Wales midfielder Robbie.
Second place in the group will not be decided until Thursday after the match between Atalanta and Villarreal was postponed because of heavy snow in Bergamo, Italy.