And the Championship side have labelled as 'preposterous' criticism of the timing of the release of a dossier to the FA regarding former manager Mackay and the club's then head of recruitment Iain Moody claiming they have known of its existence 'for many months'.
In the dossier Cardiff accuse the pair of being racist, sexist and homophobic in a series of text messages during their time together at the club.
On Thursday evening the LMA released a statement claiming Mackay was "letting off steam to a friend during some friendly text message banter". It has since backtracked on that position, but Cardiff believe its stance does not go far enough.
In a statement through their lawyers, Cardiff said: "A manager's behaviour should demonstrate to players and other employees under his control that discrimination in any form is unacceptable.
“That the LMA has sought to criticise the club for the timing of the report to the FA is preposterous, because the offensive communications have been in the knowledge and possession of the LMA for many months.
"When the messages came to light, over three months ago, the club strongly encouraged and advised Mr Moody
and Mr Mackay to deal with the issue directly with the FA.
"It was made clear to them, and their LMA appointed lawyers, that the nature of the communications meant the club was under a duty to report their findings to the FA if they did not take appropriate action themselves.
"Nevertheless, with the backing of the LMA, Mr Moody and Mr Mackay chose to do nothing. The LMA were therefore
complicit in the attempt to conceal these messages (of which there were many more than the two isolated texts acknowledged by Mr Mackay).
“The LMA is the representative voice of managers, and whilst we understand it seeks to act in the best interests of its members, one of its major aims is to "encourage honourable practice, conduct and courtesy in all professional activity”.
“We therefore find it entirely reprehensible that the LMA should itself put out a statement which seeks to dismiss deeply offensive racist comments as 'friendly banter'. 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 LMA had issued a second statement earlier on Friday reading: “The LMA apologises for some of its wording in its release yesterday, which was inappropriate and has been perceived to trivialise matters of a racist, sexist or homophobic nature. That was certainly not our intention.
“It is beyond argument that any comments that are discriminatory, even used in private, are totally unacceptable. The LMA remains absolutely aware of our responsibility to the game and to promote and uphold the highest standards of behaviour.
“The LMA will not be commenting further on the allegations relating to Malky Mackay whilst the FA conducts its investigation, other than to repeat that both the LMA and Malky will be cooperating fully.
“We will continue to work with all of the game's stakeholders to address the important issues of respect and discriminatory behaviour in all its forms.”
Cardiff then responded again via the following statement on their website: "The LMA is the representative voice of managers, and whilst we understand it seeks to act in the best interests of its members, one of its major aims is to "encourage honourable practice, conduct and courtesy in all professional activity.
Former Blackburn striker Jason Roberts, an outspoken critic of the football authorities' anti-racism measures in the past, tweeted: "The LMA said it better than I ever could. They are actually being serious! Somebody drafted that. WOW!"
And former England international Stan Collymore blasted the "institutional acceptance of the 'banter' of casual racism."
Football agent Phil Smith, thought to be the target of one of the texts, told Sky Sports News HQ he was "very surprised and a little let down" by a message which read: 'Go on, fat Phil. Nothing like a Jew that sees money slipping through his fingers'.
"Racism is completely unacceptable – and sport should lead by example as a multi-racial and multi-religious platform for those with aspirations to achieve – and this has clouded that a little."
Cardiff owner Vincent Tan sacked Mackay in December 2013, just six months after he had ended the club's 51-year wait for top-flight football. Moody had been placed on gardening leave two months previously and was subsequently dismissed.
Mackay launched a £7.5m legal claim against Tan for compensation and wrongful dismissal after his sacking but dropped the club.