Rangers winger Daniel Candeias was sent off against St Mirren for making "gestures" to defender Anton Ferdinand, referee Willie Collum has confirmed.
The Ibrox club were enraged by Collum's decision to show the Portuguese a second yellow card following the spat.
Rangers boss Steven Gerrard insisted his player had done nothing wrong and branded the dismissal "embarrassing".
The club had a 'mistaken identity' appeal dismissed, then said they would formally complain to the Scottish FA.
However, the governing body have revealed the written reasoning behind that decision, and explained that Collum deemed Candeias to have goaded Ferdinand.
The flashpoint came in injury-time as Rangers celebrated Alfredo Morelos' strike.
Candeias - who had already booked 10 minutes earlier for celebrating with the Rangers fans after scoring the opener - ran past Ferdinand while blowing kisses at him.
After a brief conversation with St Mirren goalkeeper Craig Samson, Candeias was then approached by Ferdinand, who placed the Rangers winger in a headlock before aiming a jab at his chin.
Collum booked both players, then showed a red to Candeias, who was suspended for last Saturday's 7-1 win over Motherwell.
What was the Scottish FA's written reasoning?
In their written reasoning, the SFA said Collum confirmed that he issued the yellow card because "he believed that the player had been involved in two incidents, making gestures towards the opponent, the St Mirren No 35 [Ferdinand], after the scoring of a goal and becoming further involved with the opponent as he made his way upfield after celebrating the goal".
After watching video footage of the incidents and considering Rangers' written submission and a written statement from Candeias, the tribunal found "that the referee correctly identified the player as being the player involved in the incidents".
It concluded "on a balance of probabilities, that there had been no error on the part of the referee and no mistaken identity with regard to the players involved in the incidents and specifically in relation to the player for whom the claimant had appealed".
"Therefore the determination of the tribunal was that the claim be dismissed and that the caution and dismissal, and mandatory sanction, be reimposed," it added.