Martinelli came off the bench to score late alongside Leandro Trossard as the Gunners won 2-0 at San Mames.
"I'm really happy with the result, the goal and the assist as well. To win a game (in Bilbao) is really difficult, and I thought the team did really well, especially in the second half. I'm happy to be (nominated) the Player of the Match as well," said Martinelli at the final whistle.
"When I came on, I just tried to get in behind. It was just a minute after I came on, and I wanted to just see where I could find space. I'd said to the guys on the bench that there was a huge space in behind. (Leo) saw me, it was a great ball from him and I just tried to put the ball in the net.
"For the second goal, I just tried to go past my man and look back to find someone in the box, and I knew (Athletic Club) were tired as well. I was able to find Leo, and he did the rest."
Martinelli also stated: "(Athletic Club) have a really good team and nice fans - the atmosphere was amazing - and we did well to control some parts of the game. They were playing at home, so they did well too, but I thought we were clinical and deserved to win. The most important thing was to win the game.
"When you play for Arsenal, you go to win every game, so it's really good to start the campaign with the victory.
"We know how big we are when we have this badge on our chest, and with the family we have. We're a big club and we want to win every single match."