Mackay issued a statement through the League Managers' Association late on Thursday apologising for messages "disrespectful to other cultures" which were exposed just as he was about to return to management with Crystal Palace.
But the Scot denies sending homophobic or sexist messages during text correspondence with Iain Moody - his then-head of recruitment at Cardiff - and has vowed to set the record straight once the FA investigation is complete.
The scandal has already led to Moody stepping down as Palace's sporting director and cost Mackay the chance to succeed Tony Pulis at Selhurst Park.
And the LMA's claim that Mackay was "letting off steam to a friend during some friendly text message banter" has been ridiculed by prominent figures in the game.
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."
The full LMA statement read: "In the course of a search by the club in early 2014 of 10,000 private text messages sent to and from another member of staff during Mr Mackay’s employment at Cardiff, in relation to other matters, it emerged that Malky had, it seems, sent a couple of one line texts that were, with the benefit of hindsight, very regrettable and disrespectful of other cultures.
"These were two text messages sent in private at a time Malky felt under great pressure and when he was letting off steam to a friend during some friendly text message banter.
"That said, Malky believes he could and should have conducted himself better on these two isolated occasions. The precise details need to remain private for the time being until any FA process is complete.
"The LMA does not condone in any way any potential breach of equal opportunities laws but would also point out that out of over 10,000 text messages and 70,000 documents produced over a long period of time it may not be a complete surprise that some inappropriate comments can sometimes be made by employees, like Malky, working under great pressure in highly charged situations. If Malky has caused any offence by these two isolated matters he would, however, wish to sincerely apologise.
"Malky finds it strange that these matters were only raised with the FA and in the media now, eight months after his employment ended and the day before he was reported as being offered the opportunity to become manager of Crystal Palace FC.
"Malky is also very concerned about seriously inaccurate and misleading reports of his alleged involvement in these matters in the media. It has never been alleged that he wrote any homophobic or sexist messages and he has confirmed that he did not do so.
"Further, there are incorrect and damaging suggestions that he sent a whole host of offensive and unpleasant messages that are simply not true and which give a grossly distorted and unfair view of Malky’s involvement in this matter. Malky looks forward to matters being put straight in due course, following any investigation of this matter.
"Malky cannot of course comment on the nature of any conduct or communications alleged to have been made by others.
"Malky has said that he will be fully co-operating with any FA investigation and that he looks forward to putting the record straight thereafter."
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 claim in May and issued an apology to the Malaysian businessman.