The French forward was issued with his marching orders in the 1-0 victory at Craven Cottage on Saturday for a last-minute tackle on Stanislav Manolev.
Arsenal's appeal against the mandatory ban was rejected by the Football Association and Giroud must now sit out three of the Gunners' final four games as they battle to secure a top-four finish.
And the £13million summer signing from Montpellier was left flabbergasted by the decision to uphold the original verdict.
Giroud said: "I was very surprised at the verdict as my action was unintentional.
"It does not hurt me but the rules in England are really very harsh. Very harsh indeed."