After Wes Hoolahan had clipped in Simeon Jackson's cross to put the Canaries in front after 10 minutes, it could have been easy for the top flight's bottom club to fold.
But the Latics grew into the match and eventually netted a deserved equaliser through a well-taken finish by Victor Moses in the 68th minute and had chances, notably through Hugo Rodallega, to snatch a much-needed victory.
Martinez, whose side remain bottom, but just two points between them and 17th-placed Bolton, said: "You have seen why we are in the position we are in because we cannot really show that little bit of composure or have that bit of luck in front of goal.
"We created enough chances to win and grew into the game. After giving away the early goal, I felt we were really strong, we kept the ball well, and created numerous chances.
"Clearly it was a good performance for us, but only one point to show and that is what we have to rectify from now until the end."