Giroud and teammate Francis Coquelin launched their jerseys into the crowd after fighting back from 4-0 down to level at 4-4 at the end of regulation time in the League Cup tie.
"I thought in the cup competitions in England when you draw you then replay," said Giroud. "That's why I threw my shirt into the crowd.
"I had no idea [we had to play extra time] and I only realised when one of our subs ran over to tell me.
"Luckily the man gave me back my shirt so I could carry on. I have to thank him."
Giroud has scored three goals in 14 appearances for Arsenal.