The Dundee United chairman went to war with the Hampden hierarchy this week as a row erupted over the venue and ticket allocation for the last-four clash.
And DJ reckons Thompson has a case to answer to SFA Compliance Officer Vincent Lunny over his outburst.
He said: "How can the SFA sit back and do nothing? It is absolute nonsense and he can't get away with it.
"He is on a couple of the boards at Hampden but so what? He is no different to anyone else.
"I would like to think that he is taken to task by the SFA, they can't have the chairman of a member club coming out and slaughtering them.
"That simply cannot be good for the game.
"There is no doubt in my mind that he has brought the game into disrepute and should be pulled up for it."
Just hours after he hit out at the SFA for their refusal to switch the tie to Parkhead, Thompson was forced into an embarrassing backtrack when it was revealed United admitted they would not sell all the tickets originally handed to them for the semi-final fixture.
The Arabs are furious that Rangers will receive a perceived unfair advantage by playing at Ibrox and having the majority of the crowd, but Johnstone insists the time to raise objections has long since passed.
He said: "I don't think he has done his club any favours with all the nonsense he has come out with in recent days.
"If he wasn't happy with the venue for the semi-finals, why did he not complain at the time?
"I think a lot of people wrote Rangers off and thought that they wouldn't get to this stage of the competition so it would not become an issue.
"But they are there and deserve to be there. It was announced that the final would be played at Parkhead while Celtic were still in the cup.
"Would people have complained if Celtic got to the final and played at Parkhead? The SFA made their decision at the time so everyone should just get on with it."
Meanwhile, the Rangers Supporters' Trust have hit out at comments from Thompson and Tannadice fans' chief Steven Hughes regarding their safety at the cup clash.
Thompson will not sit in the directors' box at Ibrox while Arab Trust chairman Hughes claimed United punters were 'nervous from a safety perspective'.
The Trust said: "In making this statement, Mr Hughes does not provide any evidence to back up his wildly inaccurate claims.
"Unfortunately, it would appear that the Arab Trust is actively trying to create additional tension between the clubs and fans ahead of the game.
"Furthermore, the Arab Trust does have a history of trying to antagonise the Rangers support, having called the club and the support 'huns' on numerous occasions on their official Twitter account.
"We would like to point out that, in 2011, Rangers were awarded the SPL Family Champions Award at a time when the Dundee United chairman was on the SPL board.
"Recent remarks regarding safety attributed to United chairman Stephen Thompson are also of concern. We expect the Rangers board to actively seek clarification in this regard."