Following the match, Beaton was placed under police protection after his personal information was leaked online.
The Scottish Senior Football Referees Association issued a statement on Friday condemning the treatment of officials.
"The SSFRA stands firmly alongside our colleagues following the wholly unacceptable reaction to recent refereeing decisions," the statement read.
The organization criticized the role of clubs and media figures in exacerbating the tension surrounding the referees.
"Irresponsible commentary from some managers, clubs and sections of the media has only served to fuel an already toxic environment," the statement added.
The referees' body emphasized that safety and respect must be maintained within the sport.
"No referee should be subjected to this abuse, intimidation, threats or the leaking of private information simply for carrying out their duties.
Such conduct has no place in Scottish football or society more generally," the statement said.
The association highlighted the demanding conditions under which match officials operate.
"Referees perform a difficult role in an intensely demanding environment and deserve the same respect and protection afforded to everyone else in the game.
Scottish football cannot thrive in an atmosphere where referees are subjected to personal attacks for making decisions in the course of their duties," the statement continued.
The SSFRA concluded by warning of potential future actions if the situation does not improve.
"Should this behaviour continue, we will reserve all options open to us," the statement read.
Meanwhile, Hearts captain Lawrence Shankland spoke confidently ahead of their final match at Celtic Park, noting their strong season performance.
