United dominated the possession stats on Moyes's first return to Goodison Park since leaving Everton in the summer, but they lacked a cutting edge and were ultimately undone by a clinical Toffees performance.
Moyes put Everton's two goals down to "stupid decisions" and admitted that his side weren't good enough in the final third, but believes that they put in a good performance on the whole.
"We gave away two terrible goals but prior to that we passed the ball brilliantly well, kept the ball, had great control of the game," Moyes told Sky Sports News.
"What we couldn't do is make enough chances but we had a great control and we got done by two stupid decisions. We didn't have a final through pass at times, we didn't have a final finish when they came and there weren't very many of them.
"That was the disappointing part, that we just couldn't do that in the final third but I couldn't fault how we played because we kept the ball incredibly well."
The defeat leaves United seventh in the Premier League table and now mathematically unable to finish in the top four this season.