Jose Mourinho rang the changes for the Europa League tie - most notably bringing Rashford in - but the gamble did not pay off as United were defeated by the Eredivisie side.
It was a game of very few chances, but United will probably feel that they deserved a draw, even if they didn't deserve the win.
Chances were few and far between in the first-half. David De Gea saved a curled effort from Feyenoord's Berghuis while Anthony Martial fired a shot narrowly wide.
All eyes were on Rashford during the game, but unfortunately, the teenager had a quiet evening and was subbed off in the 63rd minute as United tried to find a winner.
Ibrahimovic came on for the England international and had a chance himself but nodded his header just over the bar.
United didn't create enough chances to deseve to win the game, but they will probably feel aggreived that they ended up flying home empty handed.
Jorgensen was played in on right wing, who appeared to be in an offside position, but there was no luck in the finish that condemned United to defeat. The forward picked out Vilhena who fired past De Gea.
Mourinho's men pushed for an equaliser, but their efforts were in vain as Feyenoord held on for the win.