The Baggies secured the shock result through a Chris Brunt free-kick that deflected conveniently off Jonas Olsson. It is the first time West Brom have won two in a row at Old Trafford since 1959.
However, just 11 minutes after Olsson’s goal, United were awarded a penalty after referee Anthony Taylor ruled Saido Berahino had handled the ball in the box.
Van Persie was trusted with the spot-kick but was denied by Boaz Myhill, who condemned the Red Devils to their third straight league defeat.
The Dutch striker was given the penalty because of Wayne Rooney’s miss against Liverpool, and Van Gaal is now looking for yet another option.
When asked if Van Persie would be trusted to take another penalty this season, the United manager answered: “No, he is now at the end of the road.
“It is always [like that]. Wayne has missed also so when you miss you are at the bottom again.”
United’s poor form has given rivals Liverpool a glimmer of hope for Champions League qualification.
The Merseyside club’s 2-1 win over Queens Park Rangers on Saturday means they are now just four points behind the Red Devils in fourth with three games of the season to play.