A second-half deflected strike from Leon Osman and a Phil Jagielka header proved enough for the Toffees in a rainy encounter at Goodison Park, despite a late reply from Arouna Kone.
Wigan felt they should have had a penalty soon after Osman's opener but luck was against Roberto Martinez's men, who remain in the bottom three despite another spirited showing.
Moyes said: "Wigan played well and I have to give them credit.
"They will do the same to most teams and they don't get enough credit for the way they pass the ball and the way they play.
"I thought before half-time we were starting to look the better side but we are never comfortable because of the way Wigan play.
"We just raised it a bit at half-time and it made the difference.
"The big thing was when Ossie (Osman) went into the middle of the park - it made us play better.
"He has got happy feet. He danced through and got a shot away, obviously it took a bit of a deflection.
"The second one was a good header. It was about time a centre-half scored a goal and I'm glad Jags got it."