Cardiff City have called for League Managers' Association chief Richard Bevan to resign after the organisation described offensive text messages sent by Malky Mackay as "friendly banter".
The LMA apologised after provoking criticism from anti-discrimination campaigners over its statement.
However, Cardiff maintain that Bevan's position is now untenable.
The FA is investigating Mackay's comments as part of a dossier submitted by Cardiff alleging misconduct.
The LMA's original statement on behalf of Mackay said that two text messages sent by the former Cardiff boss to ex-Bluebirds colleague Iain Moody were "disrespectful of other cultures", but defended them as "friendly text message banter".
|Reaction to the LMA's original statement|
|Ex-Blackburn striker Jason Roberts on Twitter: "LMA actually wrote this. They are actually being serious! Somebody drafted that... WOW!"|
|Former Brentford and Torquay manager Leroy Rosenior: "If the LMA are going back into the dark ages to support people then I might have to withdraw my support."|
|Ex-England striker Stan Collymore on Twitter: "Disgraceful. Institutional acceptance of the 'banter' of casual racism."|
|Daily Telegraph's Henry Winter: "The LMA look like bumbling dinosaurs. The statement is a missive that should be filed beneath contempt."|
"We find it entirely reprehensible that the LMA should put out a statement which seeks to dismiss deeply offensive racist comments as 'friendly banter'," the club said in a statement.
"If that is the view held by the LMA, as appears from its statement, we consider that Richard Bevan's position is untenable and we call for his resignation."
The club also accused the LMA of failing to fulfil its duties.
"The LMA is the representative voice of managers, and one of its major aims is to 'encourage honourable practice, conduct and courtesy in all professional activity'," Cardiff said.
"Regrettably, we feel that the LMA has done no such thing in its representation of Mr Mackay and Mr Moody."
Troy Townsend, the education and development manager of anti-discrimination charity Kick It Out, also criticised the LMA.
"[I was] more disappointed than anything else," he told BBC Radio 5 live. "It took the focus away from Malky and the alleged texts and put the focus on the LMA and their support and backing towards him.
"I'm not sure how it got through. It's made everyone's work in this industry really difficult. It just makes it seem that what happened is acceptable."
|Mackay, Moody, Cardiff City and Crystal Palace|
|Timeline of events|
|May 2010: Malaysian multi-millionaire Vincent Tan joins the Cardiff City board as chairman.|
|June 2011: Dave Jones is sacked as manager, with Malky Mackay appointed as replacement.|
|May 2012: Tan controversially changes Cardiff's kit colour from blue to red, and replaces the bluebird emblem with a dragon.|
|April 2013: Mackay guides Cardiff to promotion to the Premier League as champions, amassing 87 points from 46 games.|
|Oct 2013: Head of player recruitment Iain Moody is suspended by Cardiff for an alleged overspend of £15m on transfers the previous summer.|
|Oct 2013: Mackay and Tan hold a five-hour meeting amid rumours their relationship is becoming increasingly strained after Moody's departure.|
|Nov 2013: Moody appointed sporting director at Crystal Palace.|
|Dec 2013: Mackay is sacked by Cardiff City following a 3-0 defeat against Southampton. Cardiff are 16th in the Premier League, one point above the relegation zone.|
|Jan 2014: Ole Gunnar Solskjaer is appointed Cardiff manager on a 12-month rolling contract.|
|April 2014: Cardiff complain to the Premier League following claims that team news was leaked to Crystal Palace ahead of their meeting.|
|May 2014: Cardiff's relegation is confirmed after a 3-0 defeat by Newcastle.|
|May 2014: Mackay and Moody apologise to Vincent Tan over the issues that led to their dismissals.|
|Aug 2014: Cardiff make allegations of misconduct to the FA, and are asked to provide evidence.|
|Aug 2014: With Mackay the frontrunner to take the Crystal Palace job, allegations of misconduct during his time at Cardiff are leaked. Palace withdraw their interest in Mackay. Moody resigns.|
In its latest statement on Friday, the LMA said it "apologises for some of its wording which was inappropriate and has been perceived to trivialise matters of a racist, sexist or homophobic nature".
"It is beyond argument that any comments that are discriminatory, even used in private, are totally unacceptable," the statement continued.
"The LMA remains absolutely aware of our responsibility to the game and to promote and uphold the highest standards of behaviour."
Mackay, who lost his job at Cardiff in December, was thought to be favourite for the vacant manager's job at Crystal Palace until the story emerged.
He says he will fully co-operate with any FA investigation and "looks forward to putting the record straight".
Moody resigned as Crystal Palace sporting director on Thursday, but has yet to comment on the story.
He was sacked as Cardiff's head of player recruitment last October after a row with owner Vincent Tan over transfer activity and joined Palace a month later.