Moyes said after the game that his side were poor throughout the 90 minutes and can have no complaints about the result.
"We were poor from the start," Moyes told BBC Radio 5 Live. "We lacked intensity and our passing wasn't quick enough.
"We had enough of the ball in the first half to create more. In the second half we tried to make those opportunities more, but defensively we weren't good enough. We weren't solid enough throughout.
"We had a lot of the ball but we didn't create enough chances. They deserved to win the game in the end."
The result means that Manchester United have won just one of their three home games this season.