Police Scotland found "no criminality" after investigating the clip, which circulated online on Saturday May 15 after the Glasgow club were awarded the Scottish Premiership trophy for the first time since 2011.
After the video appeared online, Mr Yousaf, who was Scotland's justice secretary at the time, said any player found to have been using sectarian language should be removed by Rangers.
On Monday, the MSP tweeted: "I have also been made aware of this clip, if (and I stress if) this clip is genuine then any player or staff member found to be guilty of anti-Catholic hatred should be shown the door by the Club.
"It is right Police Scot investigate & determine the facts around it."
Asked on BBC Scotland's The Sunday Show whether he had "jumped the gun" in posting the tweet, Mr Yousaf said: "I don't think anybody can accuse me of taking a side.
"I was pretty clear to say, having been asked about that video on a number of occasions that if, and I stressed very clearly, that if that video was genuine then of course action should be taken and not only did I stress, of course I mentioned that police should rightly establish the facts."
Mr Yousaf described scenes on the streets of Glasgow last weekend as "the most disgraceful and shameful display of anti-Catholic bigotry and anti-Irish racism I've ever seen".
He said: "If it had been anti-Muslim, if it had been anti-Semitic, if it had been against black people, there would have been universal condemnation."
Mr Yousaf said: "As justice secretary, I don't make an apology for calling it out and calling it what it is.
"I don't blame Rangers Football Club, in fact I actually have – believe it or not – a very constructive relationship with Rangers Football Club.
"I'm not here to defend fans or so-called fans who took part in that kind of behaviour. Let's not deflect away from what we saw on the 15th, which was simply unacceptable and would have been called out if it was any other community."
Rangers FC said on May 21 that it has initiated legal proceedings against certain individuals for comments during the week.
Mr Yousaf was asked whether he was one of the individuals, but replied: "I've certainly not received any intimation of that sort."
Scottish Conservative shadow cabinet secretary for justice Jamie Greene MSP said: "Bigotry of any sort from any quarters is wrong, no-one argues that whatsoever.
"The problem here is Humza Yousaf should not have used his position of power to pass judgement on unsubstantiated claims while a police investigation was likely. He now won't do the right thing and admit he was in the wrong.
"He has shown a complete disregard towards the police and those who were allegedly accused and since exonerated.
"The decent thing would be to accept that trial by social media on his part is not how to run a justice system - a simple apology would be a good start."