Cardiff chief executive Simon Lim criticised Mackay on Thursday for being "imprudent and careless" during the August transfer window, and blamed the Scot for his handling of the Andreas Cornelius transfer.
Cardiff claim that they lost £8.5 million on the transfer of Cornelius, who was signed by Mackay in July but returned to FC Copenhagen in the January transfer window.
The LMA were quick to come to Mackay's defence though, labelling Lim's comments as "inappropriate and unprofessional".
Mackay was sacked by Cardiff in December and there is currently a legal process underway regarding his dismissal.
"It is most unfortunate that Mr Lim has chosen to speak out in this way," LMA chief executive Richard Bevan said in a statement.
"Mr Lim is aware that there is a legal process under way between Malky Mackay and Cardiff City and it is both inappropriate and unprofessional for either party to be making public statements of this nature at this time.
"Given that Mr Lim has spoken out against Malky Mackay in relation to the acquisition of a player, however, it is only right that the record is put straight on the following two key issues.
"This is the same Mr Lim to whom, under the specific and express terms of Malky Mackay's contract of employment with Cardiff City, Malky was obliged to report in respect of all matters pertaining to the transfer of players.
"This is the same Mr Lim who, when being asked more than once, upon dismissing Malky Mackay, why he was dismissing him, said that he did not know the reason.
"All football clubs at the elite level have systems in place for corporate governance.
"Cardiff City is no exception. A manager, even in the Premier League, does not go out and "sign" players."
Cardiff appointed Ole Gunnar Solskjaer in January but their Premier League form has not improved, with the Welsh club sitting 19th – two points adrift of safety.
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