Mr Allan has expressed particular dismay at Rangers manager Ally McCoist who, when the punishments were announced, publicly called for the names of the panel – which were supposed to remain anonymous – to be made known.
Mr Allan, who makes his comments in an interview for Channel 4 news which is due to be aired tonight, says he was "astonished" by McCoist's comments.
The QC claims he had to have meetings with both Special Branch and anti-terrorist officers after police found evidence of various threats being made by groups with links to Rangers.
Mr Allan was warned not to handle incoming mail to his home and was given round-the-clock police security for weeks.
Earlier this week Rangers chief-executive Charles Green also claimed to have been subjected to threats by fans when he arrived at Ibrox.
Mr Allan tells the programme: "I wasn't ready for my family to be exposed to that and that caused me a lot of anxiety. We were given a full briefing on mail handling. I was told there would be certain items which I should under no circumstances open if they were not from a familiar source.
"I was told I should take mail into the smallest secure room with the fewest windows and have the family somewhere else in the house whilst I opened the mail."
When McCoist publicly called for the panel to be publicly named, Mr Allan says he was both worried and taken aback.
He added: "I was astonished when I saw a recording of Mr McCoist demanding the [panel's] names be disclosed and declaring he did not know who they were, and felt he ought to know."
After news of the threats emerged, McCoist said he did not regret his call for the panel members to be named but was disgusted by the threats made against them.
Rangers subsequently challenged the SFA panel's punishment – fines of £160,000 and a 12-month transfer embargo – at the Court of Session and had their appeal upheld.