The midfielder was dismissed on Saturday at the Emirates for a tackle on Tomas Rosicky, although replays showed that the decision by referee Andre Marriner was harsh.
Henry was furious with Rosicky was making the most of the challenge and also laid into Thomas Vermaelen for demanding the red card.
Agony: Karl Henry is given his marching orders at Arsenal
However, Wolves have now explained why their won't be appealing against the three-match ban. The FA's Regulatory Commission will only overturn a decision if they believe the referee has performed a'serious and obvious error'.
Boss Mick McCarthy admitted: 'Having spoken to a lot of different people over the weekend, including a number of ex-referees, I haven't found anyone yet who thinks that Karl should have been sent off.
'And that seems to be a view shared by those who have seen the incident on television as well. But having also sought advice in terms of the appeal process, we have decided to accept the punishment as it stands.
'The FA's Regulatory Commission will only uphold a claim for wrongful dismissal if they judge that the referee has committed a "serious and obvious error." Under that wording, I have been advised that any appeal would be very unlikely to succeed.
Sympathy: Mick McCarthy consoles Henry
'And if the commission also have the right to lengthen any suspension to twice the initial ruling if they believe an appeal was made which didn't have any chance of success.
'Despite our frustration and disappointment at losing Karl for three games, we can't run the risk of that ban being extended and so unfortunately we have to take our medicine and move on.'
Henry will now miss the games with Stoke, Fulham and Blackburn as they attempt to stay in the Barclays Premier League.
After the game, he said: 'It's a disgrace, an absolute disgrace. I've nicked the ball and Vermaelen has come flying in and whoever else trying to get me sent off. It's not nice to see.
'They play good football here and they're a great side. We love Arsenal's great football but when they're rolling around, getting people sent off, it makes you not want to see them do so well. Two minutes later, he's up, running around and absolutely fine.
'That's what they do here. I don't think it's pretty and it's not good. Their players moan when they get tackled, when they get hit hard, and so does Arsene Wenger. It's part of the game.
'Here in particular, Arsenal moan a lot. Their players go down like a sack of spuds. They get hit hard like other clubs do and we're hearing about it for weeks and weeks. To get sent off is a disgrace.'
Arsenal 1 Wolves 0: Henry slams Vermaelen and Rosicky over red cardGRAHAM POLL: A weekend of chaos in the Premier League. and it may only get worse with so much at stakeWOLVERHAMPTON WANDERERS FC