Aberdeen manager Craig Brown and Motherwell owner John Boyle have both been disciplined for their touchline spat at Fir Park on 2 April.
Brown escaped a ban but was censured after being found "guilty of misconduct by behaving in a disorderly manner".
Boyle was severely censured and fined £2500 for "behaving in an inappropriate and inflammatory manner".
Both were also warned about their future conduct by the Scottish Football Association disciplinary committee.
And the Fir Park club immediately issued a statement on their website, saying: "Motherwell FC is surprised at this outcome and fully intend to appeal the decision at the earliest possible opportunity."
Brown, who attended Tuesday's hearing, had reacted angrily to comments made to him by former employer Boyle after Aberdeen's 2-1 defeat.
Referee Steven McLean is not believed to have witnessed the incident, but police made inquiries about the situation, although no charges were brought.
And former Scotland manager Brown was happy to accept the decision of the committee.
"I did not think it would come to anything and I was surprised to be called at all," he told BBC Scotland.
"But I have great respect for the individuals of that committee.
"I was censured, but they took into consideration the severe provocation I was put under."
Brown left Motherwell to take over at Pittodrie in December and, along with assistant Archie Knox, has taken legal action in a bid for compensation from his former club.
Brown insisted that he had done nothing wrong in the incident with Boyle and that it was an insignificant event that had been exaggerated.
Police officers spoke to Brown after the incident, which occurred in the mouth of the Fir Park tunnel immediately after the final whistle.
"I shook hands with the chairman and subsequently it wasn't a very pleasant situation," the Dons boss said at the time.
And, asked if he'd been upset by Boyle's comments, the 70-year-old said: "Words don't hurt me."
The match commander, Superintendent Brian Connel, said after the game that no criminal inquiry had been launched following the "minor pushing".
However, he added that the police were keen to get to the bottom of the incident given their involvement in other football matters.
That was a reference to the recent problems around an Old Firm fixture, with an altercation between Celtic manager Neil Lennon and Rangers assistant Ally McCoist almost exactly mirroring what took place at Fir Park.
Lennon and McCoist were both hit with touchline bans by the SFA, but McCoist's ban was rescinded on appeal.