The Baggies recorded successive victories at Old Trafford for the first time since 1959 after Chris Brunt’s 63rd-minute free-kick deflected off Jonas Olsson and flew past David de Gea.
Van Persie had the chance to grab a valuable point for United 11 minutes later when referee Anthony Taylor ruled Saido Berahino had handled Antonio Valencia’s cross in his own box.
But Boaz Myhill saved the striker’s effort and United went on to lose their third successive match, leaving them four points above fifth-placed Liverpool with three games left.
Van Persie took the penalty because Wayne Rooney missed his previous attempt at Liverpool.
And now that the former Arsenal striker has failed to score from the spot, Van Gaal is looking for a new penalty taker.
“No, he is now at the end of the road,” the United boss said when asked if Van Persie would continue taking penalties.
“It is always (like that). Wayne has missed also so when you miss, you are at the bottom again.”
Former United midfielder Darren Fletcher was making his first return to Old Trafford since joining West Brom in the January transfer window and he admitted it was a strange experience.
“I walked out of the dressing room and I was stood on the wrong side of the tunnel and had to be told to move over to the other side,” Fletcher said. “Old habits die hard.”
Fletcher won four league titles and the Champions League during his glittering career with United and he believes improvement is needed at his old club if expectations are to be met next season.
“They have to up it a level,” the Baggies captain said. “The aim for United this season was top four.
“I hate even saying accepting top four (is okay) but the fans and everyone will maybe accept it for one season.
“But they need to be challenging for the league after that. Any United side talking about accepting the top four is just not good enough.”