David Hamilton’s comments came after at least five police officers were injured and 28 people arrested as authorities dispersed Rangers fans in central Glasgow.
The injuries to officers came after thousands of supporters celebrated Rangers’ first Scottish Premiership trophy in a decade, with many marching from Ibrox to George Square. Hours of celebrations took place in the city centre square.
However, the celebrations later turned violent, with property damage, people assaulted and missiles and flares thrown at officers, Police Scotland said.
Police Scotland’s deputy chief constable Will Kerr said on Twitter that “many more arrests will follow in the coming weeks”, while justice secretary Humza Yousaf said the scenes were “absolutely disgraceful”.
It comes just two months after similar scenes in Glasgow when Rangers mathematically secured the title on the first weekend of March.
The scenes led to similar denouncement, but Police Scotland refused to release correspondence with the Scottish Government, the SPFL and Rangers FC on the plans to police the celebrations, instead releasing 17 pages of heavily redacted emails.
Speaking to BBC Radio Scotland on Sunday, David Hamilton, chair of the Scottish Police Federation that represents rank and file officers, said the scenes were “absolutely appalling”.
He said: “[I’m] absolutely appalled. The way things unfolded throughout the day is depressing and it’s almost speechless to see that number of people blatantly ignoring all the advice, the health advice, the government advice, the police advice, even the club advice to come together.
“And then for that to escalate when police officers tried to disperse to the levels of violence we experienced is just absolutely appalling.
"I think it was predictable as soon as the league started because somebody was always going to win the league and there is always going to be some kind of celebration in some part of the country.
"It was all about a matter of mitigation. Policing in this country is, of course, done by consent and the whole strategy throughout the coronavirus pandemic has been about making sure that people take that personal responsibility and they have not done so.”
Mr Hamilton refused to comment on whether the move to disperse the crowds came too late, adding that officers on the ground were “exhausted” and that it was probably more than three officers that were injured.
Asked whether there were enough arrests, he said there would be “many, many, many” more in coming weeks.
He said: “We do not measure a policing operation by the number of arrests. What will happen now is there will be an investigation.
"There are hours of CCTV footage that will be trawled through, there will be many, many, many arrests in the follow-up investigation.
“You don’t judge a policing operation by the number of arrests. It is the outcome which is important and the main outcome of yesterday was to keep as many people as safe as possible and it’s perhaps the least worst option.
“That is a very frustrating thing for a lot of people who would have liked to have seen an absolute zero-tolerance approach, but actually we have got to look at the bigger picture here about how do we keep the most number of people safe.”
Mr Yousaf took to Twitter on Sunday morning to support Police Scotland in its approach, labelling the scenes “absolutely disgraceful” and called out reports of sectarian singing.
He said: “My full support to police officers who put in an incredible shift yesterday in very difficult circumstances.
"Absolutely disgraceful that they were subjected to the kind of thuggery we saw last night.
"Incidents of violence, disorder, anti-Catholic and any other hatred will be followed up.”
Speaking on the BBC’s The Sunday Show, national clinical director Jason Leitch also criticised the actions of the fans.
He said: “It is so disappointing to see people break rules in whatever setting and for whatever reason.
"This virus has not gone away. We’re not joking, we’re not pretending, it’s absolutely real and the risk particularly just now in Glasgow is quite high and Glasgow is fragile.
“You’ve seen us make an enormously difficult decision this week on our advice that has put a bit of Glasgow in the same level they are at just now and not allow them to move down.
"That feels like a tough day to watch that from yesterday if you are a business owner or a family waiting for lunch or dinner.
"I don’t care what it is for, the pure public health advice is the same."