Giroud played the final 28 minutes of Sunday's Premier League clash at Anfield, where goals from Roberto Firmino, Sadio Mane, Mohamed Salah and Daniel Sturridge saw the home side record a four-goal victory.
The Gunners have faced criticism from a number of quarters following the heavy loss, and Giroud has conceded that 'something needs to change' as the London club look to overcome a poor start to the new campaign.
"I was ashamed when I left the pitch against Liverpool. We have to change something. I have decided to stay. It's my choice, even if everyone does not understand it. I still want to win the Premier League here," Giroud told RMC.
Giroud, who is currently on international duty with France, rejected a host of interest to stay at Arsenal this summer.