Goals from Morgan Amalfitano and Saido Berahino proved enough for the visitors despite Wayne Rooney netting for the fifth time in as many games.
It means United have now lost three times in their opening six Barclays Premier League games and have slipped into the bottom half of the table, below the likes of newly-promoted duo Hull and Cardiff.
And Moyes is not prepared to offer up any excuses after the 2-1 loss.
"It was a poor result and a poor performance," said the Scot.
"We never really got going. We had a lot of the ball in the first half and never made many chances from it.
"They always looked a threat on the break, in the first half especially and even more so in the second half.
"We missed that spark and West Brom deserved it no question. I can't argue with that."
After putting the misery of last weekend's Manchester derby defeat behind them with an excellent midweek win over Liverpool, this latest setback was completely unexpected.
"We wanted to try to keep that momentum going," said Moyes.