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.
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.
Martinez, whose side sit 82 places above Blue Square Bet Premier side Macclesfield in the league rankings, was pleased with the win but frustrated after the Latics were unable to kill off the tie with a second goal.
"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.
"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."
- Sports & Recreation