The French international was sent off by Andre Marriner for a challenge on Stanislav Manolev during the Gunners' 1-0 win over Fulham on Saturday, receiving an automatic three-match suspension for the straight red card.
The 26-year-old has protested his innocence ever since, insisting he slipped on the ball, and after having an appeal of wrongful dismissal rejected he criticized the FA's tough stance.
“I was very surprised at the verdict as my action was unintentional," he told The Sun.
“It does not hurt me but the rules in England are really very harsh. Very harsh indeed.”
The ban means the former Montpellier man, who moved to the Emirates in a 10 million pound deal in the summer, will miss important matches against Manchester United, QPR and Wigan as Arsene Wenger's men try and secure a top-four finish.
Theo Walcott may be given more of a chance as the main striker while Giroud is missing, but the Gunners boss can also call on Lukas Podolski or Gervinho to fill the void.