The 27-year-old claims that when he was a teenager at Grenoble, his chances of playing for big clubs were written off.
"It was a long time ago - I was really young, [around] 19," Arsenal's official website quotes him as saying. "I was maybe not mature enough. I grew up step by step and proved that I could score lots of goals and did well.
"I improved myself and had the trust and confidence to continue. I succeeded in Ligue 1 and won the championship. Everything I did on the pitch is my answer for people who wanted to maybe blame me.
"I tried to do my job on the pitch and score goals. Never mind the people who did not believe in my qualities and my game. I don't care about it now."
Giroud has scored eight goals in 16 competitive matches for Arsenal so far this season.