Arsene Wenger's side became the first English team to triumph at the Westfalenstadion as Aaron Ramsey's second-half header made it 14 wins from 15 unbeaten matches away from home.
Giroud claimed the assist for the only goal of the game and with the Gunners in a healthy position at the top of Group F, the Frenchman has called on his teammates to beat Marseille to potentially guarantee a spot in the last 16.
Commenting on the performance in Germany, Giroud said: "We do what the coach asks us to do. I could have had a second assist if Aaron put his strike in the back of the net but I am glad to have participated and have assisted Aaron on his goal.
"Of course it will not be in my personal records but it is nice to have won. Few teams can win here. This is not easy, they play well at home. This is great, we are in a favorable position to win the next home game, against Marseille, and we have our destiny in our hands."