A fourth-minute header from Daniel Sturridge was enough to claim the points for the home side at the expense of United, who failed to turn domination into goals during the second period.
"I thought we played really well. We had long periods of the game but couldn't score. Apart from the lapse in concentration for their goal, we played well," Moyes told BBC Sport. "We got two or three opportunities but it was unfortunate we didn't take them."
Meanwhile, with regards to incoming players before tomorrow's transfer deadline, Moyes admitted that while he is looking to strengthen, he wouldn't be too disappointed if he failed to secure any new signings.
"From what I saw today, I'm more than happy with what I've got. It's the best we've played this season. I wouldn't be worried if I didn't add to the squad," he added.
"We will keep working for what's left of the window but I've got to say I was really happy with the performance here. Maybe in the next few hours we will get a chance to do something but we couldn't give you a heads-up on anything."
The defeat means that United have collected four points from Moyes's first three matches in charge.