Jordi Gomez scored the only goal from the penalty spot in the seventh minute, but Macclesfield will feel hard done by after they had two good penalty shouts turned down.
"Macclesfield are the ones who deserve huge credit," Martinez told reporters after the match. "We knew coming here that this football team has fantastic confidence and they are having a good run in all competitions so we knew scoring the first goal would be important but we couldn't get that second goal."
He went on: "We had a couple of good opportunities to do that but Macclesfield looked strong. They always looked like a good team and know exactly what they are doing with a bit of pace in the wide areas and trickery, they defend well so I was very impressed with Macclesfield.
"I can see why they have been successful and see very good times ahead for them in the league."
Waide Fairhurst was bundled over in the box in the first half by Roman Golobart and the ball looked to have struck a Wigan hand in the second half, but no penalty was awarded by referee Roger East.
Macclesfield manager Steve King blamed East for not awarding his side a penalty which could have changed the outcome of the game.
"I'm gutted really. I think we dominated the whole game," King said.
"They had a 10 minute spell after they scored where they kept the ball. We should have had a penalty in the fist half. I've just seen it on the TV again when Waide Fairhurst got pushed straight through the back. How he (East) has not given that, I can't believe it.
"The big decisions, he got one right and he got one wrong. Theirs was a penalty, no problem, but ours was a stonewall penalty."