Tonny Vilhena's 79th-minute strike condemned the Red Devils to defeat after Mourinho made eight changes for the trip to Rotterdam.
Manchester United boss Jose Mourinho insists his side did not deserve to lose their Europa League opener at Feyenoord. United were poor for long spells, with Anthony Martial flashing their only chance of the first half wide of the post, and Zlatan Ibrahimovic coming on after the break to head off target.
"Of course I'm unhappy," Mourinho said after the game. "We lose the game in a moment we didn't deserve to. "The second half, the game was even. We were always in control. We were trying to win, they were trying not to lose. It is double unlucky because it was a clear offside.