Gray has been granted further dispensation by the Premier League to continue as caretaker-boss at Elland Road until the end of the current campaign.
Acting chairman Trevor Birch convinced the Premier League that it was in Leeds' best interests that Gray should be allowed to remain in charge, despite not having the necessary qualifications.
LMA deputy chief executive Frank Clark now says "a precedent has been set", while the Premier League state Leeds' case is an exceptional one.
Clark said: "John (Barnwell) has worked very, very hard with the FA to improve the standard and quality of the coaching qualifications in this country, and as a consequence of that, to improve the standards in the game.
"It led to a new rule in the Premier League rule book coming into force at the start of the season; no-one can manage in the Premier League unless they have the FA diploma or UEFA pro-licence. Anything that threatens that is something that concerns us.
"Eddie has neither of those, but this is not about Leeds United and Eddie Gray and it's not about stopping people working.
"This is about protecting the integrity of the game and trying to improve the standards within the game.
"We were given assurances Eddie would only be in place on a short-term basis and we went along with that to help Leeds United. We were also given assurances it wouldn't be extended beyond the initial three month period.
"Once you start making exceptions, people will start to drive a horse and cart through the regulations.
"I am sure when John comes back he will be talking to the Premier League, because we do find what has happened disappointing, and urging them not to do something like this again in future."