Arsene Wenger's men were humbled by goals from Roberto Firmino, Sadio Mane, Mohamed Salah and Daniel Sturridge at Anfield.
A second loss in three Premier League games has intensified pressure on long-serving manager Wenger, who penned a two-year contract extension at the Emirates Stadium in May.
"I was ashamed when I left the pitch against Liverpool. We have to change something," Giroud told RMC.
The 30-year-old Frenchman also explained why he recently snubbed interest from Ligue One outfits Lyon and Marseille.
"I have decided to stay. It's my choice, even if everyone does not understand it," he said. "I still want to win the Premier League here.
"I have always said that returning to France was not an option for me, even less so in the short-term future.
"So it was not something against Marseille, because the project is very ambitious and very interesting. It was not specifically about Marseille, because I also had Lyon.
"I am very flattered to have been chased by two great French clubs."