First-half goals from Ryan Giggs and Robin van Persie proved enough to see off a dogged Everton outfit at Old Trafford, with United now 12 points clear at the top of the Premier League.
"The lads have performed brilliantly well this season," Moyes said.
"There have been parts of games where we have not done well but here is the first time I thought a better team beat us."
And Moyes is not alone in believing United look set to regain their Premier League crown.
"I think 12 points against a club like Manchester United is a big gap to make up," said the Scot.
"Football doesn't always go the way it is meant to be but it looks a lot.
"To be that amount of points ahead is a big thing at this time of the season."
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- the Premier League
- Robin van Persie
- Ryan Giggs