The SPFL are currently in talks to move one of the fixtures away from Hampden Park after both Aberdeen and Hearts expressed outrage with the original decision to host the two games at the national stadium on the same day.
Murrayfield is viewed as a viable alternative with the Hearts v Celtic match mooted as possibly moving there, though Scottish Rugby Union would still have to agree to the switch, which remains far from a formality.
While Milne welcomed the change of heart from the league, he believes measures should be put in place so this sort of thing doesn’t happen again.
He shared his concerns with the Aberdeen Evening Express, who teamed up with the Edinburgh Evening News to call for a rethink of the plans.
Milne said: “It’s good that common sense does seem to be prevailing. But once again we have embarrassed ourselves in how we run Scottish football.
“We have once again displayed to the fans that they are not being treated properly.
“Semi-finals are special games for the fans and everything should be done to ensure the fans can make the most of the day.
“This is a massive occasion and a family occasion for the fans but it’s not being treated like that by the SPFL.
“I accept we are part of that organisation so I’m not saying all the blame lies with the executive running of the SPFL.
“But we’ve got to make sure this sort of situation never develops again.
“It’s been a total embarrassment for Scottish football the fact this has become the number one topic with MSPs in the Scottish Parliament.
“Everybody and their granny has got involved in this whereas if we’d handled this properly from the outset then there would have been none of this.”