Leon Osman's deflected shot in the 52nd minute and Phil Jagielka's 77th minute header allowed the Toffees to record maximum points on Boxing Day and the showing against a difficult Wigan outfit was not lost on Moyes.
"Wigan played well and I have to give them credit," said the Scotsman.
"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."
Everton went up to fifth on the table with their eighth victory of the campaign whilst Wigan lost for the fourth time in five outings to stay in the relegation zone.