A deflected strike from Leon Osman and a Phil Jagielka header, both in the second half, proved enough for the Toffees in a rain-sodden Barclays Premier League encounter - despite a late reply from Arouna Kone.
Moyes said: "Wigan played well and I have to give them credit. I thought before half-time we were starting to look the better side but we are never comfortable because of the way Wigan play."
He added: "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."
Shaun Maloney appealed in vain for a spot-kick for Wigan after going down in a challenge from Osman and Latics manager Roberto Martinez had no doubt his side, who have now not won in six games, had been hard done to again after also being denied a penalty in last weekend's defeat by Arsenal.
Martinez said: "Shaun Maloney is not a player that looks for penalties. He is someone who once he gets in that one v one situation you know how effective he can be.
"He goes past his defender easily and there is no need for him to go down but I think if you look at Leon Osman's reaction it tells you everything.
"If you see defending a one v one in the box and someone goes down, you go mad - and rightly so.
"Leon Osman just went away and showed a face of feeling that he got away with that incident. I don't really understand what the referee saw and I am getting a bit tired of talking about these moments."