The former Cardiff boss and Iain Moody are alleged to have shared racist, sexist and homophobic texts when the latter was head of recruitment at the club.
The pair were sacked by the club last season and the Welsh club have sent a dossier to the Football Association alleging misconduct
The League Managers' Association issued a statement on Mackay's behalf which read: "If Malky has caused any offence by these two isolated matters he would wish to sincerely apologise."
The LMA claims the club searched more than 10,000 private text messages and found two from Mackay that were "with the benefit of hindsight, very regrettable and disrespectful of other cultures"
The statement added: "These were...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.
"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."
However, Mackay was said to be "very concerned about seriously inaccurate and misleading reports" in the media.
The statement continued: "It has never been alleged that he wrote any homophobic or sexist messages and he has confirmed 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 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 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.''
Press Association Sport understands Cardiff's sending of the dossier to the FA was not deliberately timed to have any effect on Mackay's candidacy for the Crystal Palace job
Meanwhile, Moody resigned as sporting director of Crystal Palace on Thursday
Source : PA
Source: PA