Bryan Oviedo hit a late winner at Old Trafford last night.
Moyes said: "I'm disappointed to lose but that is the way the game goes sometimes.
"The game was tight. We missed some opportunities to score and Everton took it when they got their opportunity."
Asked if the loss hurt him more than usual as it was to Everton, he added: "It doesn't hurt any more.
"I know they are a very good team, Everton, with very good players.
"You would imagine it is a sore one when it is your old team. That is the way it is."
Despite his years of service to Everton, the club's fans gave Moyes - who made a joint bid that was deemed derisory by the Toffees for Marouane Fellaini and Leighton Baines over the summer, and eventually secured the former for United - a hostile reception during the match.
And asked about that, the Scot said: "It is not important.
"Everton supporters supported their team well tonight.
"They had to come here and make sure they got right behind their team and they did that."
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