Moyes will take over from United manager Alex Ferguson at the end of the season and was given an emotional send-off by Everton supporters on Sunday.
Belgium international Kevin Mirallas scored both goals in a victory which ensures Everton will finish the season above city rivals Liverpool in consecutive top-flight seasons for the first time since 1937.
And even though Everton should have won by more than a two-goal margin, Moyes was happy that his last game on home turf ended on a winning note.
"It was a perfect finish," said Moyes, whose final game as Everton boss will be against Chelsea at Stamford Bridge next Sunday.
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"More important for me was how well Everton played. I thought we played like a top team not one in fifth or sixth. We'd have been a match for any side on that performance.
"It was a really emotional occasion. All the stewards were standing clapping me when I came in, and I didn't know what to do.
"The chairman took a big gamble. Giving a young British manager an opportunity to work. He needs a lot of credit for that.
"I'm really fortunate to get the reception I got. I am gobsmacked and thankful and humble for what the people of Everton have shown me.