Malky Mackay is "very concerned about seriously inaccurate and misleading reports" in the media and has said he will fully co-operate with any Football Association investigation.
However, the League Managers' Association have said text messages sent during Mackay's employment at Cardiff were 'regrettable'.
Earlier, Iain Moody resigned as sporting director of Crystal Palace as the Football Association revealed it was investigating allegations of misconduct during his time at Cardiff.
The FA is looking at a dossier sent to it by Cardiff which alleges misconduct by Moody during his time as head of recruitment at the club. The dossier also alleges wrongdoing by the Mackay, who had been close to becoming Palace's new boss following the exit of Tony Pulis last week.
The LMA put out a statement on behalf of Mackay after it was confirmed that the Football Association were investigating a dossier sent to them by Cardiff reporting sexist, racist and homophobic comments by the former Bluebirds boss and Moody.
The LMA said it wished to clarify the position in relation to recent reports and speculation regarding matters alleged to have arisen during Mackay's time at Cardiff.
A 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."