The runaway Premier League leaders went ahead through Ryan Giggs in the 13th minute and Robin van Persie added a crucial second shortly before the break.
Moyes said: "We didn't start the game very well and Manchester United were really good in the opening period.
"The goal just before half-time made it really difficult for us. But full credit to the lads; we stuck at it, kept going, never gave in and we are a bit disappointed we never got a goal in the game."
Moyes was forced to reshuffle his defence shortly before kick-off with the unwell Sylvain Distin replaced by Johnny Heitinga.
"It didn't help but I wouldn't want any excuses," said Moyes. "Johnny is an experienced player and he would have been delighted to play. That's the way it is and that's why you have got a squad of players and they have to be ready to play."
However, the Scot was unhappy with his side's defending for Van Persie's goal.
He said: "I can't understand why we were so high because we wouldn't work that way - we don't coach that way.
"I thought we had been having a really good passage of play without really creating an awful lot. But I have no idea how we got ourselves so high up and square at the back and obviously we gave them an opportunity to run through or pass through us."