Brown was seen smiling and waving Ryan Kent off the park after the Rangers winger was shown a second yellow card by referee Clancy for a nondescript challenge on the Dons captain in the 83rd minute.
Gers legend McCoist joked that the pair were "skipping off" the pitch after the 1-1 draw that saw the Ibrox side drop points for the first time under Giovanni van Bronckhorst.
"It was that obvious the two of them were doing the Gay Gordons, skipping off that park, the referee and Broony," McCoist told talkSPORT.
"It was absolutely embarrassing, it really was.
"Ryan Kent got sent off for two bookings and neither of them were bookings, there you are."
Aberdeen earned a point after Lewis Ferguson’s spot-kick cancelled out Ianis Hagi's opener, which came seconds after the Dons were denied a penalty at the other end when goalkeeper Allan McGregor tripped Ryan Hedges.
"I have to stand corrected and tell you Aberdeen should have had a penalty," McCoist added.
Former top flight referee Charlie Richmond also criticised the performance of Clancy, claiming that Brown had duped the whistler into sending Kent off.
“[Scott] Brown has played for it and Kevin has bought it," he said.
“Overall, I thought he tried to referee the occasion rather than the actual game.
“Aberdeen vs Rangers is very volatile but when you look at the individual incidents, there’s a lot of things that he could have man managed.
“I thought he was a little inconsistent and had a poor game.”