Police investigations are continuing into violence following Hibernian’s win over Rangers in the Scottish Cup final.
Rangers said its players and backroom staff were assaulted when fans invaded the pitch at Hampden Park on Saturday.
The former chief executive of the Scottish Football Association (SFA), Gordon Smith, warned that Hibs could face SFA sanctions over the incident.
Eleven people have been arrested for minor offences, according to Police Scotland.
Speaking to BBC Radio Scotland’s Good Morning Scotland, Mr Smith said news of the violence was receiving international attention.
He said: “It is sad because this is going around the world – the world has seen this and it is a bad reflection on Scottish football and I think possibly there will be rules reset for future games.
“They [the SFA] will definitely be looking at this and bringing in some measures that would try and avoid this happening again.”
An investigation by the SFA is likely to look at ways the violence could have been avoided, he added.
“It might have helped if there had been more of a police presence around the ground just to stop this happening because I think it was mainly stewards that were there and I don’t think there was much of a police presence at that point when the final whistle blew,” Mr Smith said.
Rangers have demanded an independent investigation into the “shameful scenes” following their 3-2 defeat.
It was the Edinburgh club’s first cup win since 1902.
In a statement released on Sunday, Rangers criticised the response of the the SFA, Hibernian, First Minister Nicola Sturgeon and the BBC to the incident.
There has also been some criticism of the police response to the pitch invasion.
But Calum Steele, of the Scottish Police Federation, told Good Morning Scotland that the police response was “nothing short of remarkable”.
He said: “The speed and the skill, the agility and indeed the brilliance with which the police officers from the police service of Scotland brought events under control is something that should be praised to the highest heavens.”
He added: “It almost doesn’t matter what the police service had done, they would have been criticised regardless.
“Had there been hundreds or many, many more hundreds of police officers on the track before the final whistle in a sea of yellow jackets and possibly even shields, I suspect today’s discussions would have been about the very heavy-handed approach that the police had taken in what was otherwise a very enjoyable football match.
“The police tend to be damned if they do, damned if they don’t.”
Police brought horses on to the Hampden pitch to control the crowds, including a section from the Rangers end of the ground.
The pitch invasion delayed the presentation of the trophy and there was no lap of honour for Hibs players.
Rangers players were not able to pick up their cup final medals.
After Saturday’s game, SFA chief executive Stewart Regan said it was “appalled” by the scenes of disorder and the “contemptible behaviour that ensued”.
“The Scottish FA, along with Police Scotland and the stadium management, have initiated a full investigation into the scenes that unfolded to understand how such a volume of supporters were able to enter the field,” he added.
The Scottish government said it is also “liaising closely” with the organisations involved in the inquiry.
A spokeswoman added: “Violence has absolutely no place in football, either on or off the pitch.
“The First Minister condemns unreservedly any act of violence or disorder by anyone who attended the Cup Final.
“It is for the police to take action against anyone suspected of having committed an offence.”