The League Managers Association released a statement on Mackay's behalf describing alleged racist, sexist and homophobic language as "friendly text message banter".
The organisation apologised for the choice of wording today.
"I've certainly never said personally the word 'banter', so that's something that I feel was.. I think the overall statement was very, very accurate," Mackay told Sky Sports News. "I think that word was wrong and the LMA soon realised that and they've tried to correct that today.
"I think a lot of that statement was factual and I think there's various parts of the statement that show there was absolute contrition on my part in terms of it was wrong. I think the use of that word was wrong as well and as I say, the LMA have a very long-standing reputation in the game which is very good.
"I think every manager in the LMA in the country backs the LMA and backs Richard Bevan and the very good work they do for this country in all works of life. They realised they made a mistake quickly and they changed it. I don't think they meant any offence in any fasion as far as that's concerned, but let me re-iterate that at no time did I think that what I said was anything other than inappropriate and for that I apologise."
Moody has not made a public statement as yet, but resigned from his position as Crystal Palace sporting director yesterday.