The Toffees clinched all three points through a late header from Tim Cahill.
“I thought it was a fabulous performance and result. If ever a team and its character was going to be judged it was today after the defeat (by Villa),” said Moyes.
“It would have very easy to get down but they bounced backed immediately. Those players played well and in the end deserved the victory.”
Everton played without a single striker due to injury problems.
“At times it was 4-4-2, at times it was 4-5-1, at times it was 4-6-0. So there you go, work that out,” he added.
“I have always said Tim can play up front and he scored with a great header, which he has been threatening to do for a month or so.
“As for Leon Osman, he had a fitness test and should not have played today. But we have a group who always want to play.
“They play when they are injured and play out of position. They get on with it and it is great when you have a group like that.”