Wenger lodged an appeal against the automatic three-game ban that followed the Frenchman's dismissal for his challenge on Fulham's on Stanislav Manolev, with the Arsenal boss bemused by the rejection of his version of events.
"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's completely accidental and a very minor incident," Wenger told the official Arsenal website.
When asked whether he felt the appeal against the red card fell into the 'frivolous' category that could have encouraged the FA to extend the ban on Giroud, Wenger was equally forthright.
"Honestly nobody could accuse you of a frivolous appeal when you see what happened again," he added. "I thought frivolous appeal, no - but will they overturn the red card?' For me that was 50-50, but we were never in doubt of it being seen as a frivolous appeal.
"That's why I decided to appeal. I'm sad that it didn't work but we have to cope with it. We will have to do without him and we will do it."
Wenger is due to face the media for his pre-match press briefing ahead of Sunday's game against newly-crowned Premier League champions Manchester United at 09.00 BST on Friday.