The Scot did not discuss his appointment as Sir Alex Ferguson's successor, but did speak about his time on Merseyside and revealed he was set to stay at Goodison Park
The 50-year-old agreed to succeed Sir Alex Ferguson on Thursday after it was announced that the veteran manager would be stepping down at the end of the season.
But he only wants to reflect on his time with the Toffees, and this weekend's game against West Ham, until he is officially unveiled by the Red Devils when he takes charge on July 1.
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"I wasn't planning on leaving. My contract was running out but we were planning for pre-season. All we've ever done here is keep planning," he told reporters.
"I hope [the Everton fans] react [to the news] the same way they did when I first stepped through the door. But, with football fans, you can never tell.
"If they don't I will totally understand as I am a football fan, myself. You support your team. That's what you do.
"But I am going to be standing in the same position and trying to make sure we stay focused and headed in the right direction.
"The big thing is to finish with as many points as we possibility can as there is a real outside chance of a place in Europe."
Moyes went on to further praise the supporters, saying that he would not have been able to stay at Goodison Park for so long without their support.
"The fans have been great to me from day one here," he continued. "I would like to say thank you for that support they've always given me.
"I remember my first game against Fulham, the reception they gave me, I was relatively unknown. They've been great. It's not normal now that a manager stays in a job for 11 years, it's less likely than it's ever been; without the backing of the supporters I'm sure that wouldn't have happened."
The former Preston North End boss is hopeful that his final two games in charge of Everton are not dominated by talk around his future, but also acknowledged that there will be many people in the frame to replace him.
"The players this year have been exceptional and I would hate to think Sunday and next week are about David Moyes," he added.
"I'm sure there will be lots of good people interested in this job and no wonder, because it is a great place to work."