After getting back to winning ways in the Capital One Cup against Liverpool on Wednesday night, United were expected to comfortably secure another home victory over the Baggies in the Premier League on Saturday.
But a solid Baggies defensive display, along with some impressive counter-attacking football, proved too much for the Red Devils to handle, and Moyes felt his side got what they deserved.
"Disappointing performance, disappointing result. We never really got up to speed," Moyes said.
"We had a few chances, but West Brom held their shape and defended well.
"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."
The United manager introduced Adnan Januzaj at half-time in place of Shinji Kagawa, but the change had little effect on proceedings.
"I just tried to find another way, change things from the first half," Moyes explained.
"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.
"I thought young Adnan came on and did really well.
"I have a strong team here at United, some good players, so I am in no doubt we will put it right.
"We will just go out and try and win the next one."
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."