The LMA released a statement on Thursday insisting that Mackay is sorry for any offence caused by alleged derogatory text messages that have been made public.
But the press release was viewed as highly offensive by a series of well-respected football figures, with the LMA, who were left red-faced, describing Mackay's conduct, while regrettable, as "friendly text message banter".
Mackay and Iain Moody are reported to have exchanged a series of insulting texts to each other while at Cardiff City.
The pair were both sacked by Cardiff last season and the Welsh club filed a dossier to the Football Association (FA) alleging misconduct between the duo that hit the headlines as Mackay was seemingly on the verge of taking the vacant managerial post at Crystal Palace.
The original LMA statement said that Mackay had, "it seems", sent text messages that were "very regrettable and disrespectful of other cultures", but referred to the immense pressure that the 42-year-old was under at the time.
But the LMA moved away from their initial statement on Friday and claimed any discriminatory comments "are totally unacceptable".
"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," the organisation's latest statement read.
"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 co-operating 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."
