The Scot was ruled out of the running for the vacant Crystal Palace manager's job on Thursday after the Daily Mail published details of texts he sent while in charge at the Welsh club.
While Mackay, who left Cardiff under a cloud last year following a falling out with owner Vincent Tan, apologised via the LMA for the messages he called "disrespectful of other cultures" the LMA said they were "friendly banter."
The statement said that Mackay had been under pressure at the time of the messages and that he was "letting off steam to a friend during some friendly text message banter."
That statement has been widely criticised by anti-discrimination campaigners within the game, and the LMA today felt compelled to apologise for how the first release had been worded.
A statement on the LMA website read: “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.
Former Cardiff manager Malky Mackay is facing allegations of misconduct
“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.”
The LMA are now apologising for the inappropriate nature of their apology for a member's inappropriateness?
High-profile cases of racist language involving the likes of Chelsea skipper John Terry and former Liverpool striker Luis Suarez have blighted the game and the Mackay incident prompted leading anti-discriminatory organisation Kick It Out to say the game was "tainted" by racism and homophobia.
"These revelations are further confirmation of how football is tainted with racism, sexism, homophobia and antisemitism, and the culture which continues to exist throughout the game and in wider society as a whole," a statement said.
"The reality is that these views are most dangerously held by those people in positions of power, and the football establishment knows and condones it.
"The governing bodies and the clubs must denounce such attitudes prevalent in the game, and take the appropriate action. If these types of exchanges made privately make it into the public eye, the individuals concerned must accept the full consequences of their actions.
"Kick It Out now awaits the outcome of The Football Association's investigation."
- Sports & Recreation
- Society & Culture
- Malky Mackay