Goals from Franco Di Santo and Arouna Kone were enough to prove there is life after Victor Moses for the Latics.
Speaking about the game, Martinez said: "I am delighted, as we knew we were coming in the worst possible moment to play them due to their winning momentum from their achievements to get into the Premier League.
"They put us under massive pressure early on, and from then on we composed ourselves and slowly grew into the game.
"It was a well worked performance and we had to be perfect in many aspects.
"The strikers live on great finishes and scoring goals. They did huge jobs for the team, and the goals were their reward."
Next up for the Latics is the trip to play Nottingham Forest in the Capital One Cup on Tuesday in a game that is being televised on Sky.
Martinez is likely to play a number of fringe players for that one and supporters will get a good chance to see the likes of Callum McManaman and Jordan Mustoe in action.