The Latics scored first through Jean Beausejour in the 18th minute before Davide Santon responded for the visitors with a little under 20 minutes remaining.
However, Arouna Kone was able to give Wigan a vital victory with a very late winner and Martinez was thrilled to see the character and determination of his players pay off.
"It was a day that we knew we needed to start showing a different type of character at home," said Martinez whose side sits 18th on the table.
"Our home form hasn't been good enough in terms the points we have collected not because of the quality of our play.
"We had to show an incredible character to get the winner and probably we got a little bit of luck, which is probably what we deserved because over the course of the season we've not been a lucky side.
"The reverse fixture at St James' Park we had a couple of really difficult decisions (Maynor Figueroa was controversially sent off) to take so it was really pleasing to get three points so late in the game."