Benjamin Sesko struck on 71 minutes to earn the points for United.
Afterwards, a frustrated Moyes said: "I'm not happy with the scoreline that's for sure. You have to win games if you are going to keep moving on. We've not been doing that as much as we'd like, especially here (at home).
"We've lost narrowly to United, we beat them narrowly at Old Trafford earlier in the season. I though we did well in lots of bits, we get done on the counter and they get the one goal. We put in effort to score but lacked quality to get the goal.
"We weren't organised well enough off the ball. I have to praise them (United) for their quick attack. We knew that would be the case, they've been doing that really well. They have forward players who have to ability to run away fast and make chances. Most of the game we controlled it pretty well but in that one moment we switched off and it gave them that opportunity.
"Their goalkeeper (Senne Lammens) did a great job, made an amazing save from Michael Keane, looked as if he could take every corner kick. I thought there was a goal in there for us but we couldn't quite do it.
"They (the fans) saw us pushing United to the last minute, but we couldn't quite get it. I don't think we deserved to lose the game tonight. We are disappointed, but there are good things to take away as well."