Cardiff chief executive Simon Lim said that the Scot, who was dismissed in December, and former head of recruitment Iain Moody were guilty of "imprudent and careless management", citing the substantial financial loss incurred as a result of the Cornelius transfer.
The 20-year-old Dane was signed by Mackay for just under £10m before the start of the season, but left the club during the January transfer window to return to FC Copenhagen.
And Lim, who praised the transfer business carried out by new manager Ole Gunnar Solskjaer, released a statement on Thursday that was highly critical of the former incumbent.
"We took the hard decision to incur these losses for the good of the club," the statement on the club's official website read.
"To commit the club to a significant cost and liability over a five-year contract for one player is not prudent, especially as he was not to contribute to our success now, but was for the future.
"Indeed, in the case of Andreas Cornelius, who cost the club in total just under £10 million, we realise a large loss in excess of £8.5 million.
"The key shareholders have made their dissatisfaction of such a huge loss known to the board of directors, which they believe is due to imprudent and careless management undertaken by the previous football management.
"The new structure, headed by the chairman with our new manager Ole Gunnar Solskjaer, has given comfort to our shareholders that the process is prudent, transparent and professional."
Lim also stated that Solskjaer had the full backing of chairman Vincent Tan, who had a very public falling out with Mackay.
He added: "Tan Sri Vincent Tan, through the board of directors and with their support, is 'encouraged by the work done by manager Ole Gunnar Solskjær in the January transfer window'.
"Solskjaer was instrumental in attracting top professionals who have the experience and the willpower to make an immediate impact in the club's desire to maintain its Premier League status.
"The process was transparent, creating value for the club throughout all of the transactions."
