The Scottish FA are to investigate comments mate by Boyd regarding John Beaton on Celtic TV during the side's 2-1 win extra-time win over Championship side Dunfermline Athletic.
After being denied a late penalty Boyd went on a rant about Beaton, querying if the decision was premeditated.
He said: "If he doesn't know that's a penalty he should not be in the middle of the park refereeing a football game.
"He'll probably be welcomed down his pub tonight again."
He added after the match: "Old law, new law, no matter what kind of law, that is a penalty. How John Beaton hasn't given that... we've seen it before from referees like this. John Beaton not giving us penalty, absolutely stunning decision... standing alone there, I wonder what his thoughts are.
"I'm mystified... I'm not mystified. John Beaton as though it was a premeditated decision not to give that penalty because it was so late in the game, I'm not sure.
"It's come off his arm. Regardless of players down or whatever, he's not given a drop ball. So he's seen it hit the hand of the Dunfermline player and it should be a penalty. Outrageous decision from John Beaton.
"We've not played well, but once again a decision from a referee may cost us in this game, hopefully we'll go on and beat not the 10 men, not the 11 men of Dunfermline, but the 12 men."
Hartson backed the Celtic ambassador on Twitter by replying to a post from a Celtic fan.
A supporter tweeted a video of Josh Meeking's handball in the Scottish Cup semi-final between Celtic and Inverness CT in 2015. It was a decision which enraged fans.
The post was accompanied by the caption: "Tom Boyd has spoken what a lot of Celtic fans think, there are some Referees who give Celtic nothing, I don't go in for grand conspiracy theories but some decisions are simply beyond explanation".
Hartson responded by saying 'Been there seen it done it' with the thumbs down emoji.