Piara Powar, executive director of European football's anti-discrimination body FARE, said the FA should charge Liverpool with bringing the game into disrepute. Powar said Dalglish's comments had been "undignified" and their response had damaged the club's brand across the world.
Powar told Press Association Sport: "I think the FA should come back now and be very clear that Liverpool could be construed to have brought the game into disrepute by the way in which they have consistently undermined the judgement and by Kenny Dalglish's comments."
He added: "Liverpool have been too keen to support their man and in doing so have whipped up a sense of paranoia amongst their fans.
"This is not the Liverpool FC that we have applauded in the past for their support for a whole range of issues.
"The responses from Kenny Dalglish have been undignified, the way in which they have dealt with the whole matter has been unprofessional.
"For the club to so aggressively militate against what looks to most people is a considered judgement from the FA leads to a potential for anarchy."
Powar said reaction from his colleagues in other parts of the world made him believe the affair was damaging Liverpool. He added: "They have damaged their brand, no question. There is no question that Liverpool do have a global appeal, but I have emails from colleagues in Africa asking me what the hell is going on.
"I think people will be watching this and I believe there is no question that their plans for global expansion will have been damaged by this.
"That's not to say they cannot come back from this but it has done them a lot of damage and they have not conducted themselves in a very palatable way."