Alex Munoz struck before the break for the Canarians, with Girona losing Juan Carlos to a red card midway through the second-half.
Afterwards, Martinez says it was a team performance that produced the victory.
He stated,"It's easy to say, but winning against this rival, and especially after such a long time without doing so at Gran Canaria, with a clean sheet, is something important. It's true that we found it difficult to relax in the game, they started better than us.
"When the team doesn't have fluidity with the ball, it has to be well positioned and we did. We grew in the game, we finished the first half very well, we went from less to more. In the second half, the team deserved the second goal, we had very clear chances to make it 2-0 and close out the game. I think the team was very focused in the last few minutes."
Martinez also said, "This is not just about one or two names, this is a victory for everyone, this victory only has one feeling and no surname. There are players who have not played today who will be important in the future.
"Players who have played 5-10-15-20 minutes or however many are needed and have been important in getting the three points and it is important for us to see where we were two weeks ago... if on the day of my presentation they had told me that we were going to make 6 out of 6 in two games, we would all have signed for it."