A stunning goal from Hatem Ben Arfa early in the second half cancelled out Steve Sidwell’s deflected 19th-minute opener as United looked to be getting on top.
But captain Fabricio Coloccini lost Hugo Rodallega for Fulham’s winner, with the forward heading a Damien Duff free-kick past Tim Krul.
Alan Pardew: “We keep putting in performances, but not getting what we want.
“It is difficult, but you can’t concede soft goals at this level.
“We can’t blame anyone but ourselves. We’ve got to work on that.
“We conceded a soft second goal when we had the game by the scruff of the neck.
“We were playing well, pushing on, and it was a poor goal.
“Then you’re away from home, and you’ve got to score three goals to win. It’s difficult.”