The First Minister spoke out after a number of Celtic supporters held a violent protest outside the stadium on Sunday following a shock 2-0 home defeat to Ross County in the League Cup. A group of fans clashed with police outside the ground and Celtic players had to be escorted from the stadium after being targeted with missiles.
Three police officers were left with minor injuries following the incident.
Speaking at a daily coronavirus briefing, Ms Sturgeon described the scenes at “despicable” but refused to single out Celtic fans and instead issued a reminder to fans of all Scottish football teams for their behaviour, including Glasgow rivals Rangers.
She said: “I don’t care if you’re a Celtic fan, a Rangers fan, Ayr United fan, no fan of football at all, anybody who attacks police officers is doing wrong and that is pretty despicable.
“I would say that across the board regardless of football or any other sporting affiliation.”
Ms Sturgeon reiterated there were restrictions in place which limits gatherings outside to just six people from two households.
Appearing on talkSPORT, McCoist took aim at the First Minister for mentioning his former club Rangers, as well as Ayr United, when alluding to the chaotic scenes outside Celtic Park.
McCoist, who scored 355 goals in a fifteen-year spell at Rangers, said: “Getting back to Nicola, I don’t know what she was doing bringing Rangers and poor Ayr United into it.
“But that’s probably a topic for another discussion.”
Ms Sturgeon was also hit by backlash on Twitter.
One user said: “Celtic fans protested against Celtic players and management, why bring Rangers and Ayr Utd into the discussion it has nothing to do with those clubs Nicola Sturgeon?”
Another said: “Nicola Sturgeon it was Celtic fans that had violent demonstrations against their manager and players. Why did you mention Rangers and Ayr United. I am 62 years old and do not recall anytime that Rangers fans have been involved in protests like the ones on Sunday.”
A third said: “So how does Nicola Sturgeon condemn the actions of the Celtic fans. She mentions Rangers. What a sad state the SNP really are.
“Any reason for the mention of Rangers and Ayr United? Both of which quite clearly had absolutely nothing to do with the riots. Unless you count results.”
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Celtic confirmed they would be launching an investigation.
The defeat to Ross County ended a 35 consecutive cup victories and 11 domestic trophies in a row.
The Hoops are also targeting a historic 10th league title in a row but trail Rangers by 11 points in the table.
In a statement, the club added: “For players and a management team, who have given so much in recent years and have delivered 11 consecutive trophies, to require an escort from Celtic Park while being targeted with missiles is simply unacceptable.
“While we understand that only a small number of people were involved in this behaviour, some of the actions this evening, which have obviously left our own players shaken, cannot be condoned in any way.”