The manager left the Toffees after 11 years in charge of the side to take over at Old Trafford following Sir Alex Ferguson's retirement at the end of last season.
The Scot told the club's website: "First of all, the game is not about me, it's about Everton and Manchester United.
"I go there as manager of Manchester United and I'm delighted to be that. I was proud to be manager of Everton at that time but my job now is to make sure I get a result for United.
"The Everton fans were always terrific in my time there, very supportive and always right behind the team. We go there with a great away record and go there trying to keep that going."
Moyes returns to Goodison Park with United on Sunday.