Giroud was shown a straight red card by referee Andre Marriner in the final minute of last Saturday's 1-0 win at Fulham for jumping into a challenge with defender Stanislav Manolev.
The Arsenal boss initially indicated he felt the dismissal had been warranted, but the club decided to issue an appeal, which was rejected by the Football Association on Tuesday, after which the Frenchman said: "I am sad that it didn't work, but we have to cope with it."
Wenger must now re-evaluate his attacking options for crucial games against newly-crowned champions Manchester United on Sunday, then at QPR and at home to Wigan before Giroud, who has netted 17 goals, will be eligible again on the final day at Newcastle.
"It is a blow that we cannot have him available. We will have to do without him and we will do it," Wenger told Arsenal Player.
"It is a harsh decision. After the game, I was a little bit less convinced that he didn't deserve the red card, but having seen it again, I feel it is completely accidental and a very minor incident."
Wenger could opt to deploy Theo Walcott, currently Arsenal's leading scorer with 18, down the middle against United, looking to stretch the defence with his pace, or hand Lukas Podolski - who has netted 14 times this season - the chance to impress in a central role.
Whatever attacking line-up Wenger decides upon, the Arsenal boss knows there will be little margin for error given their slender one-point lead over fourth-placed Chelsea and two-point advantage over north London rivals Tottenham, albeit having played a match more than both teams.
Goalkeeper Lukasz Fabianski will again miss out because of a cracked rib, but otherwise Wenger reported no fresh injury concerns from the 1-0 win at Craven Cottage - which was a ninth win in the last 12 league games.
Arsenal are expected to mark United's achievements with a guard of honour before the match, when former Gunners captain Robin van Persie has been warned to expect a heated reception from the Emirates Stadium faithful following his controversial £24million move last summer.