The Baggies won at Old Trafford for the first time since 1978 thanks to goals from Morgan Amalfitano and Saido Berahino, sandwiching Wayne Rooney’s fifth goal of the season.
Moyes felt United were in control for some periods of the game but was unhappy with the overall display and lack of cutting edge.
"It was a poor result and a poor performance – we never really got going," he told MUTV. "We lacked an intensity and spark to our game, and in the end they deserved the win, I can’t argue with that.
"In the first half we had a lot of the ball and tried to move it – we probably controlled a lot of the game – but I thought for all our possession we didn’t create a lot of opportunities. And when we did, we didn’t take them.
"They had a couple of chances on the break and the more we went for it, the more chances they seemed to get.
"We had plenty of forward players out there but we're just not opening teams up. I'm concerned after today but there are a lot of games to go and we'll try to put it right."
As Moyes sought to rescue the game in the second half, he brought on fit-again Robin van Persie and Adnan Januzaj, with