It was a test of character for Arsene Wenger's side, who eventually came through after the introduction of England duo Jack Wilshere and Theo Walcott, whose deflected effort with five minutes left proved decisive.
Giroud maintains if the Gunners are to force their way back into the top four of the Premier League and look to continue their cup run in the quest for a trophy, they have to produce the same effort in every game.
He said: "We didn't start the game as we wanted because we didn't put in a good commitment and not really enough determination.
"I play better not when I am angry, but with determination, this is very important in football. We want to get six points against Liverpool and Stoke to reach Tottenham and fourth place (in the Premier League), then we will play and see where we get."
Giroud, 26, continues to grow into his role at the head of the Arsenal attack and enjoys the challenges of the English top flight.
"I chose this championship because there is more intensity, more physically, you have to be ready in the athletic way," he said. "I like it, but I like to play good football as well."
Wenger believes Giroud offers his Arsenal side an attacking focus.
"He is all you need to play as a centre-forward, a physical presence. Usually we would go for a more mobile player, but he gives us something different."
Captain Thomas Vermaelen is expected to recover from an ankle injury to be in contention against Liverpool on Wednesday.