A number of Light Blues representatives attended a disciplinary meeting at Hampden earlier this week where they answered five charges of bringing the game into disrepute.
The charges focused on the publication of an official statement calling into question Collum’s suitability as a top flight whistler.
Scottish football’s governing body confirmed on Thursday that two charges - criticising officials in a way that indicated bias and not acting in the best interests of Scottish football - had been proven, resulting in two separate fines totalling £6,000. Two breaches were not proven and a fifth was withdrawn.
The charges stemmed from a strongly-worded statement published by the Ibrox club after Collum sent off Daniel Candeias during the 2-0 league win over St Mirren at the Simple Digital Arena in Paisley.
The statement read: “Rangers are extremely disappointed with the decision of the Scottish FA’s Judicial Panel to dismiss our appeal against the second yellow card shown to Daniel Candeias in the closing seconds of last Saturday’s match against St Mirren.
“Rangers afforded the governing body the opportunity to let common sense prevail and we are surprised they have chosen not to do so by correcting what was, and what remains an inexplicable decision by the match referee, Willie Collum.
“If one of these decisions is obviously wrong, it must be possible to correct that mistake. It is wrong that players’ livelihoods and careers can be impacted without the opportunity of redress, especially when the official responsible for the miscarriage of justice is allowed to continue as though beyond question or reproach.
“It defies belief that this same referee, who got it so blatantly wrong last Saturday, is awarded one of the biggest matches in Scottish football this weekend while Daniel Candeias is denied the right to go to his work. This, frankly, is unacceptable.
“Furthermore, it is understood that a number of people within the Scottish FA are in no doubt Mr Collum’s judgment was flawed and Rangers shall also now be submitting a formal complaint about the performance of this referee. The manner in which he reacted to an incident involving our player made it obvious he did not give due consideration to his decision.
“This is by no means the first time errors of judgment have been made in matches involving this official and clearly there is an underlying issue which requires to be addressed.”
The outburst, published on the club’s website, drew the attention of the Scottish FA’s compliance officer, who issued a notice of complaint.
Rangers later lodged a formal complaint against Collum, and publicly criticised the appeals process after failing to overturn the second yellow card received by Candeias in the match with St Mirren.