New £12million signing Samir Nasri scored the only goal of the game to defeat West Brom at The Emirates.
Gallas told Sky Sports: "It was our first game and I think we did a good job.
"It was important to win the game. We were a bit nervous, especially they played well with the long ball, and it was not easy for us.
"It was not easy for us but it was very good because we wanted to win our first game and start well.
"I think we have a lot of hard work ahead of us because it is just the beginning of the season."