Bilic’s newly-promoted put in a terrific display but ultimately left Manchester empty-handed after a 1-0 defeat as key penalty decisions went against them in each box.
Referee David Coote had awarded the Baggies a second-half spot-kick and a chance to take the lead after Bruno Fernandes brought down Conor Gallagher, but overturned his decision after consulting the pitchside monitor, adjudging that the Portuguese had got a touch on the ball before felling his opponent.
"I'm very disappointed with the decision,” Bilic told BT Sport. “I felt like 'small West Brom'.
“All those crucial decisions went against us. I've watched it a few times and it's a clear penalty. I don't understand why he overturned it."
Bilic’s misery was compounded less than ten minutes later when United were given a penalty at the other end for a handball against Darnell Furlong.
Goalkeeper Sam Johnstone brilliantly saved Fernandes’ effort, only to be penalised for coming off his line, and the Portuguese converted at the second attempt.
"It's a handball,” Bilic conceded. “It's a bit unlucky but it's handball. Before that it was a clear foul on Conor Gallagher. Instead of 1-0 for us, it's 1-0 for them. When you play against Manchester United away it's a huge difference."
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