Malky Mackay has apologised for sending two one-line text messages he admits were "disrespectful of other cultures".
The former Cardiff boss and his ex-Bluebirds colleague Iain Moody are alleged to have shared racist, sexist and homophobic texts.
But Mackay, 42, says his texts were part of "friendly text message banter".
"If Malky has caused any offence by these two isolated matters he would wish to sincerely apologise," read a League Managers' Association statement.
The pair were sacked by Cardiff City last season and the Welsh club sent a dossier to the Football Association alleging misconduct.
The LMA says 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".
"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," added the statement.
However, former Football League player and manager Leroy Rosenior, a leading voice for Show Racism the Red Card and a trustee of anti-discrimination body Kick it Out, said he was disappointed with the LMA's use of the word "banter".
Rosenior, who is also a member of the LMA, said: "If the LMA are going back into the dark ages to support people then I might have to withdraw my support.
"In over 70,000 text messages I've sent I've never used inappropriate language and I'm sure neither have the vast majority of people."
The LMA statement said it did "not condone any potential breach of equal opportunities laws" but 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".
|Former Reading striker and anti-racism campaigner Jason Roberts on Twitter|
|"LMA actually wrote this. They are actually being serious! Somebody drafted that... WOW!"|
Mackay was said to be "very concerned about seriously inaccurate and misleading reports" of his involvement.
"It has never been alleged that he wrote any homophobic or sexist messages and he has confirmed he did not do so," said the statement.
"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."
Mackay, who lost his job at Cardiff in December, was thought to be favourite for the vacant manager's job at Crystal Palace.
He says he will fully co-operate with any FA investigation and "looks forward to putting the record straight".
Rosenior continued: "If Malky did use a couple of texts, as he admits to in the statement, then I'm disappointed and I think it needs to be dealt with not as something swept over or as a bit of banter.
"I know the LMA are trying to protect their member but in doing so I feel they are almost abusing another member, like myself."
Moody resigned as Crystal Palace sporting director on Thursday, but has yet to comment on the allegations.
He was sacked as Cardiff's head of player recruitment last October after a row with owner Vincent Tan over transfer activity.
Here are some of the text messages alleged to have been shared by Moody and Mackay, as reported in the Daily Mail on Thursday:
- "He's a snake, a gay snake. Not to be trusted." Referring to an official at another club.
- "Not many white faces amongst that lot but worth considering." Referring to a list of potential signings.
- "Go on, fat Phil. Nothing like a Jew that sees money slipping through his fingers." On football agent Phil Smith.
|Mackay, Moody, Cardiff City and Crystal Palace|
|Timeline of events|
|May 2010: Malaysian multi-millionaire Vincent Tan joins the Cardiff City board as chairman.|
|June 2011: Dave Jones is sacked as manager, with Malky Mackay appointed as replacement.|
|May 2012: Tan controversially changes Cardiff's kit colour from blue to red, and replaces the bluebird emblem with a dragon.|
|April 2013: Mackay guides Cardiff to promotion to the Premier League as champions, amassing 87 points from 46 games.|
|Oct 2013: Head of player recruitment Iain Moody is suspended by Cardiff for an alleged overspend of £15m on transfers the previous summer.|
|Oct 2013: Mackay and Tan hold a five-hour meeting amid rumours their relationship is becoming increasingly strained after Moody's departure.|
|Dec 2013: Mackay is sacked by Cardiff City following a 3-0 defeat against Southampton. Cardiff are 16th in the Premier League, one point above the relegation zone.|
|Jan 2014: Ole Gunnar Solskjaer is appointed Cardiff manager on a 12-month rolling contract.|
|April 2014: Cardiff complain to the Premier League following claims that team news was leaked to Crystal Palace ahead of their meeting.|
|May 2014: Cardiff's relegation is confirmed after a 3-0 defeat by Newcastle.|
|May 2014: Mackay and Moody apologise to Vincent Tan over the issues that led to their dismissals.|
|Aug 2014: Cardiff make allegations of misconduct to the FA, and are asked to provide evidence.|
|Aug 2014: With Mackay the frontrunner to take the Crystal Palace job, allegations of misconduct during his time at Cardiff are leaked. Palace withdraw their interest in Mackay. Moody resigns.|