The Red Devils had to play most of the game with 10 men after Juan Mata was sent off in the first half following two yellow cards in quick succession.
Salomon Rondon scored the winner in the 66th minute at The Hawthorns when he fired home Sebastien Pocognoli’s left-wing cross.
The result left United sixth in the Premier League table and three points adrift of the top four, with Manchester City boasting a game in hand on their rivals.
And former Arsenal striker Henry accepts that Sunday’s result will come as a big blow for the Red Devils.
Speaking on Sky Sports after Sunday’s game, Henry said: “It is a massive setback.”
He continued: “They had a lot of possession, they arrived here on a high, but they are still in the mix.
“They played a lot of games and it was always going to be difficult here, but it is a blow.”
Manchester United take on Liverpool in their Europa League clash at Anfield on Thursday night.
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