After a tight game of few chances, Arouna Kone scored the all-important winner with nine minutes remaining.
The win - Wigan's third league victory in four matches - saw Martinez's side climb into 17th in the table above Aston Villa on goal difference.
Martinez told Sky Sports: "It was very important (to win) as you can imagine, I think the points they are vital to try to increase the points tally.
"But today was more important than that. Today was to find a way to perform after an international break which historically for us has been very, very difficult.
"Today we had to find that extra character to keep a clean sheet against a Norwich side who are the best team in the Barclays Premier League in dead-ball situations and we all know how organised they are and how well they do to keep a clean sheet.
"So I'm extremely, extremely proud. I think it is one of those performances that probably we weren't at our best in terms of the style and the fluent possession that we always have because we had a few tired legs as you can expect.
"So today to perform in that manner, to find a way to keep a clean sheet, to find a way to score that all-important goal and restrict Norwich to no shots on target, is a phenomenal effort and a great result."