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.
"There were signs but the performance went on to be a poor one. I'm concerned after but only because we didn't play well. There's a lot of games to go and we can put it right."
First United need to start scoring. They have still not found the net in open play since the opening day of the season, with Rooney converting another long-range free-kick.
Even the second-half introduction of Robin van Persie and Marouane Fellaini failed to change the game in United's favour.
"It's not from the lack of trying or lack of forward players," said Moyes.
"It's just not quite opening teams up the way we would like and we need to try to do that better."
Yet again, Moyes appeared to show a lack of faith in Japan star Shinji Kagawa.
After starting him on the left-hand side of midfield, Kagawa was then hauled off at half-time, replaced by 18-year-old Adnan Januzaj.
"I just decided I wanted to make a change and inject a little bit of something," said Moyes.
"Adnan showed what he can do in periods. We want Shinji to feel he's getting an opportunity to show what he can do and his best position may be number 10.
"But even for Japan he plays off the left as well so it's not something which is strange to him or a position he's not used to.
"There's a lot of competition here and we want to push each other."
United must now lick their wounds ahead of Wednesday's Champions League encounter with Shakhtar Donetsk in Ukraine, when Van Persie is likely to start after shrugging off his groin problem.
"I hope so," said Moyes.
"He's not missed an awful lot. His injury was a small one. Our plan was to give him some time today."
Although the result will come as a huge shock to a team that won the title by 11 points last term, West Brom boss Steve Clarke was not surprised.
"Anybody listening to me before the game would know I said I was coming here to be positive to try to play," he said.
"The players must have been listening as well because they did that.
"Against the reigning champions you have to play almost the perfect game.
"We could have had more. We looked a threat every time we went forward.
"It's not about the fear factor. West Brom has always been capable of coming to these sorts of places, defend doggedly and nick a winner or a draw.
"But I want to try to win the game and we achieved that."
Clarke had particular words of praise for his goalscorers, including Amalfitano, a deadline-day loan signing from Marseille.
"His English is OK," said Clarke. "He understands more than he lets on. When you tell him he's done well he always understands.
"He's a player that I'd seen play on a number of occasions, bright lively and has the flair to create going forward."
But 20-year-old Berahino was the hero, keeping his cool to beat De Gea from Amalfitano's pass.
"He deserves his place in the team," said Clarke of the England Under-21 international. "He's made an impact and as you've seen he's got a goal in him."