"This goal has taken the pressure off me," he is quoted as saying on Arsenal's official website.
"It's done, I have my first goal. But it has to be the start of a beautiful adventure.
"Even unconsciously I was thinking about this first goal. I tried not to think about it but my family, friends and a lot of people were talking to me about it."
Giroud added that his maiden strike has enhanced his confidence.
"For a striker, it's always good to find the net again," said the Frenchman. "I have an assist already this season but it's not like a goal.
"For a striker, it's important for the confidence. I hope many more will follow.
"I want to play week in, week out, find my rhythm and keep scoring. I am convinced that with some perseverance, it will come."
Giroud joined Arsenal from French champions Montpellier in the summer.