Everton beat the Latics with goals from Leon Osman and Victor Anichebe, with Antoine Sibierski netting a late effort for Wigan.
Moyes said: "We did the job, our play merited more goals than we did get. At 2-0 I felt it could go to 3-0 rather than them scoring. Apart from the few minutes after their goal, I felt we were pretty comfortable."
"Ossie's goal was terrific, a header from that range. You have to give him credit for getting his effort on target and in the place he managed to put it," Moyes added.
"Some people might question the goalkeeper's positioning, but I would rather praise Ossie for the execution of the goal. It was that good I doubt the 'keeper could have got it.
"In the end we deserved that win and it has got us off to a very good start to the season."
Wigan chief Chris Hutchings was far from impressed with his side's defending at key moments.
He said: "We went behind to what we felt was a lucky goal, but they all count. Then we had a good spell and couldn't score.
"And what you mustn't then do is to allow Andy Johnson time to turn in the box and play a pass across like he did, the goals we conceded were poor.
"New players, particularly in defence, take time to gel. But we were still far from happy with the goals we conceded.
"But I felt we did well. Jason Koumas on his debut was excellent, he is the sort of player who has you on the edge of your seat in expectation.
"Sibierski, too, he scored our goal and has the mark of quality that we need and know will improve us.
"Pre-season can be false, you don't know really how well you are doing. So I was pleased with a lot of what I saw, the effort we put in and the positives out there.
"We need points on the board, but there are plenty of other teams who have lost so we now must look to a couple of home games coming up."