Scottish Football Association chief executive Stewart Regan says events at Wednesday's match between Celtic and Rangers were "embarrassing".
The SFA is to launch an inquiry after three players were sent off and angry scenes broke out at the final whistle.
"I was saddened and deeply embarrassed to witness the scenes during what's supposed to be Scottish football's flagship fixture," said Regan.
"The SFA condemns the inflammatory and irresponsible behaviour."
In a stormy Scottish Cup fifth-round replay, which Celtic won 1-0, Rangers' Steven Whittaker and Madjid Bougherra were sent off - both for second yellow cards, of which there were 13 in total.
Their team-mate, El-Hadji Diouf, was also shown a red card after the full-time whistle for dissent towards the referee.
Earlier in the game, Diouf had been involved in a touchline altercation with Celtic manager Neil Lennon, who then had to be pulled away from Rangers assistant manager Ally McCoist at the end of the game after reacting angrily as the pair shook hands.
Regan says the events during and after the match do little for the reputation of football in Scotland.
"These images were broadcast around the world and shows our game in a poor light," he said in a statement.
"I acknowledge the pressures of expectation on both clubs, but last night's behaviour crossed the boundaries of acceptable conduct at a football match."
Regan said indicated that the two Glasgow clubs had to shoulder more responsibility for what happens in and around their local derbies.
"We have already launched an investigation into all incidents that occurred and will do everything in our power to ensure there is no repeat," he said
"The events at Celtic Park, however, run deeper than the Scottish FA's disciplinary procedures.
"The unedifying sight of two of the country's most recognisable and respected coaches engaged in an angry confrontation was not only unsavoury but exacerbated an already incendiary atmosphere inside the stadium and throughout the West of Scotland.
"The clubs have a duty of care to ensure that the image and integrity of the game is upheld at all times. This was not adhered to last night.
"It is incumbent on Rangers and Celtic to ensure a far more responsible level of behaviour."
The one plus point for Regan was the way in which referee Calum Murray handled the match under pressure.
"Last night's actions - which culminated in three red cards and 13 cautions in total - also re-emphasised the ongoing lack of respect for our match officials," added the SFA chief.
"It was a source of comfort that at least one person retained his composure amid last night's chaos.
"Only a matter of months after our referees withdrew their labour, we had to witness the match official, Calum Murray, being manhandled, while another player who had been dismissed brazenly walked to his own supporters in defiance.
"It is a tribute to his professionalism that Calum and his team kept calm.
"A degree of faith in Scottish football was lost last night. All parties must work together to help restore it."