The club is also being questioned by Jim Jefferies, their former manager, over the decision not to renew Billy Brown's contract, claiming his close friend would have continued as No.2 for free.
Hearts, who are still in the throes of administration, announced on Tuesday that Brown will leave after Saturday's match against St Johnstone in Perth due to what has been described as cutbacks.
Bryan Jackson, the administrator from BDO, revealed yesterday that Southern and Murray had agreed to a temporary reduction in their earnings but, as Hearts lurch closer to relegation, Mackay has questioned the way the club is being run.
"[Former manager] John McGlynn lost his job just before the League Cup final last year when the Lithuanians were still here and we have an assistant manager who was in the dugout when Hearts won the Scottish Cup in 1998 being relieved of his duties just weeks before we have a chance to get back to another national cup final.
"If you asked any football person before a ball was kicked this season whether Hearts could survive in the top flight, their answer would have been no. Some people within the club know nothing. Hearts are the only club in Scottish football to have a director of football yet they can't sign players. We have a guy who worked in PR who is now the managing director and someone who was an academy director who is now a director of football.
"Their pay cuts are too little, too late. How long have Hearts been in administration, yet they're just taking pay cuts now? It's a token gesture. It seems to be a reaction to their roles being questioned on a national level in the media and not just by myself. I have no agenda, it's about the club being run in a professional manner; in administration or not."
Jefferies, the Dunfermline manager, who led Hearts to the Scottish Cup in 1998, believes there is more to Brown's imminent departure than meets the eye. "There is no way it has been done for a cost-cutting exercise, that's just nonsense. I'm quite sure if they had approached Billy and said, 'we still need to make cuts', Billy would have offered his services for nothing. At this stage in his career, it's not about money, it's about going in there and helping a young manager who is thankful for the experience that Billy has.
He endorsed Mackay's view on Murray's role. "They're the only club in the top flight with a director of football yet they can't sign players. If they didn't have money you would think that position would be a bit of a luxury. They wanted a change for a reason and someone in there has made that decision."
In acknowledging yesterday that Southern and Murray had accepted pay cuts, Jackson said: "They have both agreed, very kindly, to take a cut in their salaries. I would say they were meaningful enough and, from my point of view, I appreciate the gesture. They have contracts but they have agreed to it."