The former Everton boss said he is worried about his side's start to the season, adding that he is finding it difficult to select his best team given his large squad.
The former Everton manager, who took over from Sir Alex Ferguson after the veteran's retirment at the end of last season, has come under increasing pressure, and he said the home defeat to the Baggies has left him worried about his team.
"I'm concerned after today but only because we didn't play well," he told reporters. "There's a lot of games to go and we'll try put it right in the games coming up. It was a poor result and a poor performance. We never really got going. We had a lot of the ball in the first half, but we didn't create any chances from it. They always looked a threat on the break, especially in the second half."
Moyes made seven changes to his side that lost its last league match in humiliating fashion at local rival Manchester City, and he noted that he is yet to work out his best team because of the large squad he has at his disposal.
"I don't think there is one best team. I think there are lots of best teams at Manchester United," he added. "We look to play all the players and I think we did that today. We changed it in midweek and gave the bulk of them another chance today to make sure it wasn't just one good game. I'll get to know them a lot better and the more I see them the more I'll get to know them."
West Brom coach Steve Clarke was understandably thrilled with his side after its first league win at Old Trafford since December 1978, and he praised his players for following his game plan to a tee.
"I think anybody that listened to me before the game will know I was coming here to be positive and would try to play. Thankfully my players were listening because they did that." he said. "I thought we were tremendous from start to finish. We did everything almost perfectly, and when you come to a place like Old Trafford you have to almost play the perfect game. I think we did that."