The Government has vowed to operate within court guidance when publicising referendums after promotional material for the children's rights vote was deemed not fair, equal, impartial or neutral.
Mark McCrystal, the engineer whose legal challenge exposed the error, called for resignations over the misuse of some of the 1.9 million euro publicity campaign.
"The Government has gone well beyond its powers in doing serious damage to democracy and freedom in this country. This has to be addressed seriously," he said.
"I think heads should roll big time on this. I think it's an intolerable situation for this to happen."
Mr McCrystal contested that the Government was in breach of rules set down by the 1995 McKenna judgment which bars public funds being used to promote a vote one way or another in a referendum.
Material was carried in a booklet delivered to every home, a website and adverts.
Among the issues raised in the case was the wording of phrases such as "Protecting Children", "Supporting Families", images depicting a smiley face and an inference in the material that a referendum was needed.
In a statement, the Government said it was carefully studying the Supreme Court judgment, delivered in full after an initial ruling over a month ago.
It said it welcomed guidelines from the court and would in future act within the limitations.
"The court unanimously acknowledged that the principle enunciated in the McKenna judgment stands as firm as ever, but the modes through which information is conveyed are very different to those which were operating in 1995," it said.