Dundee asked the SPFL for their Premiership clash with Aberdeen on Boxing Day to be postponed after they were left decimated following a positive Covid-19 test in the squad.
It led to James McPake registering 41-year-old Mackay so he could take a place on the bench for the 2-1 loss at Pittodrie.
Halliday called for the SPFL to give clubs more help in such circumstances and believes such incidents lessens the standing of the game in Scotland.
"I’m not being funny, I lived in England for six years and used to have arguments week in week out, because of the way that people look at our game," he said.
"Look at Dundee, they’ve got a 41-year-old assistant manager who has been retired for six years and needs to go on the bench. It’s not ideal for anyone and it’s not Dundee’s fault.
"That’s something we need to look at and if club’s need help they get help but as players we want to play games.
"What surprises me is that teams are obviously looking for a bit of help from the governing bodies, St Mirren and then Dundee on Boxing Day. My understanding is that if they ask for the games to be postponed with the amount of players they have available I thought the league was going to help them in that.”
He added: “I don’t quite know the ins and outs but what I will say is that if it means we’re postponing these two games and then in three weeks time the crowds are full again I’m all for it."
‘Not hopeful’ of crowds returning
Halliday, speaking after Hearts defeated Ross County 2–1 in front of an empty Tynecastle Park, stressed the need for fans to be at games.
He has backed the decision to bring the winter break forward so when the Premiership returns in the middle of January there won’t be restrictions on crowd numbers, but fears that it won't be as straightforward as that.
“Whether that happens we’ll soon see but even on Sunday, listen I can’t stress that no footballer wants to play in that,” he said.
"As much as the second half is down to us I don’t think that quite happens if it’s a full house. They’ll let you know once you make two or three bad passes and it’s time to get your concentration levels.
If in three weeks time the stands are full again I’m all for it but I’m not hopeful.
"I just don’t think we can, can we [extend the break further]?
"There is going to be a tailback in terms of fixtures already, but we’ve been pretty fortunate. I do think it’s up to the players and every club to be as diligent as they can, even Joe Public out there, you still have to respect the rules and restrictions and try and isolate.
“We have been pretty fortunate but hopefully we’ll start to see cases quieten down over the next few weeks."