N'Zogbia is not set to miss three games for violent conduct as the Latics look to push themselves away from the relegation zone.
Speaking about the headbutt that saw N'Zogbia dismissed, Martinez told the Wigan Evening Post: “We got away with it today, because football is a team game and his team-mates helped get him out of jail.
“It was a difficult game for Charles, because he was getting very rough treatment from the Arsenal players, but that is no excuse and he let the whole team down.
“We’ll deal with the situation internally, but for now I’d rather look at the positives – such as beating Arsenal in the second half with 10 men.”
The Latics will now miss N'Zogbia for the games against Newcastle United, Bolton Wanderers and Aston Villa.