In a game that was completely overshadowed by VAR - the Baggies were awarded a penalty in the 53rd minute when Bruno Fernandes fouled Conor Gallagher in the box.
Referee David Coote pointed to the spot but was then told to look again at the decision and decided to overrule himself after heading to the monitor.
But a host of pundits, including former United star Rio Ferdinand and referee Peter Walton said the official got the decision wrong.
To compound the Baggies' misery, United were then given a spot-kick of their own when Juan Mata’s cross hit the arm of Darnell Furlong.
Sam Johnstone saved Fernandes first penalty.
But VAR judged the keeper had strayed from his line with Fernandes then scoring at the second attempt.
Albion still had chances to pull level with David de Gea making a great save to deny Conor Townsend while Callum Robinson hit the bar.
But Bilic’s men just couldn’t get the goal their performance deserved.
“I thought the big decisions went against us,” Bilic said.
“In that second half I felt we were small West Brom, you know.
“Big decisions, not small decisions, went against us completely.
“It’s a penalty on Conor Gallagher, I am very disappointed that he overturned that decision.
“Then the next for them, a few minutes after, it is a penalty. It is. It’s re-taken, it should be because they are the rules.
“But that penalty shouldn’t be given in the first place because there was another foul on Conor Gallagher. I am very disappointed with that.
“If that happens in any game - if that happens in the Championship - you are in trouble.
“But when it happens at Old Trafford it’s like, bang - it’s almost game over.
“But we didn’t stop. We continued, we didn’t sink.
“We tried to equalise and were unlucky with a couple of chances with Conor Townsend and Callum Robinson.
“We needed Sam (Johnstone), like we do in every game. He was brilliant.
“I am so disappointed with the result but I am very pleased with the performance.
“I am very pleased with the performances recently, with the way we are training.
“I am pleased with the work rate, I am pleased with the atmosphere.
“And I told the guys if we play like this, but improve our quality, then we are going to have a chance in every game.”