In a candid interview with the BBC, the former whistler also criticised the performance of Andrew Dallas during Rangers’ 4-0 win over St Mirren, as well as the Scottish FA for his continued selection for big matches.
Saturday’s game at Ibrox saw the referee award four penalties to the home side, three of which were disputed.
Conroy said: “It wasn’t good and I think it won’t come as a surprise when I say that. It shouldn’t come as a surprise to Andrew either, it wasn’t good.
“I’m surprised that Andrew was put in such a big situation considering what’s happened to him in previous weeks. If the referees keep making mistakes like this then it is everybody’s reputation that’s on the line.
“If that had been me or several other contemporaries of mine I don’t think I’d have been awarded such a big game so soon after recent events. You would need to ask people above me if it is true but that is certainly the perception.
He added: “There are some people who go through a lot quicker than most and probably a bit quicker than is healthy because it is an apprenticeship. You need to put in the hours, you need to put in the years before you can start going into such situations that the big games present.”
Conroy revealed that there are more Rangers fans in the referee ranks than Celtic supporters. However, he disagreed with the assertion that there is corruption among referees and with any conspiracy theories.
Officials are not required disclose which team they support, although Conroy had no problems with admitting he is a Celtic fan.
“I don’t like conspiracy theories,” he said. “I think it is an awful easy excuse to explain things away.
“Was Andrew biased, was he corrupt? I don’t think you can say that. He certainly didn’t have a good game, that’s without a shadow of a doubt. Did he do that deliberately? I’m not so convinced.
“But I do know there are conspiracy theories and there always will be and unfortunately that’s part of what we play into as well when we have so many bad performances.
“Someone had asked me previously if I had ever encountered cheating openly by refs. No is the honest answer. Things happens far too quickly, they are far too unpredictable.”
Conroy has asked for the SFA to be more open with mistakes and for referees to be taken out the limelight when after a poor performance.
“It’s not good just now,” he said about the standard of refereeing. “However the organisation do it, we certainly have to address all these mistakes which keep on happening.
“The perception would be that despite making all those mistakes that it’s fine he’s (Dallas) going to carry on getting games.
“I’m assuming that the SFA are accepting that Andrew made those mistakes. There has to be consequences to that, whether you get a few games in the lower divisions to keep you out the headlines, to give you chance to recoup and reflect.
“I think that has to be much more open than it seems to be just now.”