Latics headed for Tyneside hoping to extend the Magpies' miserable run in the Premier League to five consecutive defeats, but found themselves facing an uphill task within 12 minutes after Maynor Figueroa was dismissed.
The defender was shown a straight red card for a challenge on Papiss Cisse which also resulted in a penalty from which Demba Ba fired the home side into a lead they never surrendered.
But Martinez said: "We will look into it. The red card obviously has to be because he is stopping a clear goalscoring opportunity.
"It's difficult to see how a striker is going to score a goal if the ball is divided between two players.
"Both players are allowed to challenge for the ball. As a defender, you are always going to be strong; as a striker, you are going to invite the contact.
"It is shoulder to shoulder for me. What is important is that the contact was shoulder to shoulder, and that's allowed.
"In the laws of the game, you are allowed to challenge for the position. We will have to look into it if we can appeal for the red card."
Wigan might have been reduced to nine men before half-time had referee Mike Jones not taken a lenient view of Gary Caldwell's challenge on Ba having already been booked for a challenge on the same man.
Martinez said: "I thought it was a yellow card, if am honest with you, the second one. I don't think the first one was a yellow."
Having fired the home side into a lead from the spot, Ba doubled the Magpies' advantage with 21 minutes gone when he converted the rebound after keeper Ali Al Habsi could only parry full-back Davide Santon's strike.
Despite their numerical disadvantage, the visitors continued to play a full part in the game, but they were vulnerable on the counter-attack and were caught 19 minutes from time when Frenchman Sylvain Marveaux, producing his best display to date in a black and white shirt, picked out substitute Gael Bigirimana, and he curled home a third.
Asked about Ba reaching 10 goals for the campaign, Newcastle boss Alan Pardew said: "He has been brilliant for us.
"At times, he is important in the dressing room and everything else that he brings to the club.
"I have tried to encourage him to be more vocal in the dressing room because he's a leader, but the 10 goals is a nice target for him.
"But I was so pleased for [Vurnon] Anita. To come from the Dutch champions to come to us having not been part of what was a great season last year, he must have thought, 'What have I done?'
"I am very pleased he won tonight, and I honestly thought he was the best player."
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