Supporters Trust spokesman Mark Dingwall said the Hampden boss' position was "untenable" after it was ruled the governing body had no power to hand down a 12-month transfer embargo to the Ibrox club.
Rangers were heavily censured by an independent three-man panel after being found guilty of a series of rule breaches while disgraced chairman Craig Whyte was in control.After the decision was upheld by an appeal panel, Rangers went to court, with Lord Glennie ruling in favour of the Glasgow giants yesterday afternoon.
Fifa have already voiced their concerns over the club taking the SFA to court, but Dingwall believes it is the Hampden hierarchy that the game's governing body should be upset at as Regan comes under mounting pressure.
He said: "Mr Regan was the leading advocate of changing the SFA procedures.
"We were told that what had gone before was essentially useless and unfit for purpose and that he was the man to change it. Guess what? The first real test of his system and it has failed, it has collapsed.
"It is not just the credibility of the system, it is the credibility of the man who hoisted the system on Scottish football that has been called into question.
"This has been deeply unpleasant for Rangers, but it has been a disaster for the SFA. It has held the SFA up to ridicule and I think Mr Regan's position is untenable.
"He presented himself as a competent reformer, he promised a lot but, in the end, he has delivered a shambles."
The SFA said they will evaluate the situation. A spokesman said: "We are surprised by the verdict especially since the original sanction was imposed by an independent panel chaired by a leading QC and upheld by an Appellate Tribunal chaired by a Supreme Court Judge."