Prior to the match, Martinez's side were six points from safety with 10 matches left to play.
However, they brought themselves back into contention for a place in next season's Premier League thanks to a late strike from Arouna Kone.
"Three points at this stage of the season is huge. We went through a period where we have to score a second goal otherwise it becomes difficult. But I could not be prouder of the character - especially at this stage of the season," the Spanish boss told BBC Sport.
"Without scoring the second goal when we were leading 1-0, we found a way to win. The character was magnificent. They were very strong with good individual players who are a real threat."
After the international break Wigan will play host to Norwich City.