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Wales are "furious" players were threatened with bookings if they wore the OneLove armband at the World Cup.
Gareth Bale was among a group of European national captains who planned to wear the armband during games to promote diversity and inclusion.
But they were told by world governing body Fifa they faced "sporting sanctions" if they did so.
Football Association of Wales chief Noel Mooney told ITV it was a "terrible" decision.
"For months and months we have known we were going to wear the OneLove armband and they certainly did," said Mooney.
"To lay that one on us is pretty cheap and pretty low, to be frank. We are really disappointed by that attitude.
"We have been absolutely furious about this. We have given Fifa everything we have got in terms of how furious we are about this decision. We think it was a terrible decision.
"I understand why everybody would be upset about the OneLove armband not being there but there was no way we could ask Gareth Bale to take a yellow or red card at his first World Cup, how could you do that?
"Anybody who thinks the player can just take a red card like that, they don't really understand the psyche of a professional athlete who is going out to play the biggest moment of their lives.
"We didn't back down. We had to look at the sporting sanction that was there.
"We had said we would accept fines, whatever sanctions came, but when it turned at the very last moment to specific sporting sanctions that would have stopped our players taking the field of play potentially, that is a different thing. It was done so late."
Wales had the rainbow flag on prominent display at their training base in Qatar on Wednesday, sending a defiant message to World Cup organisers.
Mooney also criticised Fifa over fans entering stadiums being forced to remove rainbow bucket hats.
That has included former Wales captain Laura McAllister who was told to remove her rainbow bucket hat as she attended Wales' opening 1-1 draw against the USA.
McAllister, the former Sport Wales chair and Fifa council candidate, is gay and said the security at the stadium was "heavy handed. It was quite intimidating".
A professor at Cardiff University's School of Law and Politics, McAllister is also currently board director at the Football Association of Wales Trust and deputy chair of Uefa's Women's Football Committee.
"I was in the stadium and I started to get messages and texts saying people were having their bucket hats taken off them," said Mooney.
"I heard shoelaces were taken off people, I heard wristbands were taken off people. You couldn't make it up.
"We were told this was going to be a really inclusive, welcoming, warm World Cup. That is not what I have seen, I have to say.
"To have our fans having their bucket hats taken off them is just appalling. We are seeking clarifications on that.
"We have asked Fifa to come back to us today with some clarification for the Iran game that our fans can wear whatever they wish.
"Their voice was taken away, the players' voice was taken away by the armband. For that we are deeply disappointed."
Germany players covered their mouths during the team photograph before their World Cup opener against Japan.
Manager Hansi Flick said it was "to convey the message that Fifa is silencing" teams.
Germany's football association, the DFB, also says it is investigating whether Fifa's threat to sanction players for wearing the armband is legal.
Football's world governing body threatened bookings for any players who wear the rainbow armbands intended to promote diversity and inclusion.
Wales' Bale had planned to wear the OneLove armband, along with England's Harry Kane and the captains of Germany, Belgium, Denmark, the Netherlands and Switzerland.
The Football Association of Wales, which has requested a meeting with Fifa over the incidents, had said on Monday: "We're frustrated. We're disappointed.
"But we remain with the belief that football is for everyone and stand with our LGBTQ+ members of the Welsh football family."
Mooney, however, told ITV there is no chance that Wales would leave Fifa.
"No, the global game is here as one family," he said.
"Like any family we have bad moments, of course we do. This is a bad moment for us because we think that one love message of inclusivity was a really important message for us to get out there.
"That being taken away from us was not a good moment."
No disciplinary action will be taken against Germany and as it stands Wales have not been reprimanded for their stance.
The Dragons are next in action on Friday against Iran, beaten 6-2 in their opening game by England.