Some Celtic football fans sang "if you hate the Royal Family clap your hands" throughout a minute's applause in memory of the Queen before their away match against St Mirren.
Supporters of the Glasgow-based club also held up a banner containing the same phrase at the stadium in Paisley.
The club is already facing UEFA disciplinary proceedings after supporters held up a "F*** the Crown" banner during Wednesday's Champions League draw against Shakhtar Donetsk in Poland.
Celtic's manager Ange Postecoglou said he preferred not to comment when he was asked about the chant after his side's 2 - 0 defeat.
He said: "I addressed all that in two press conferences, I'm not going to do it in three.
"I get why the interest is there, but I'm a manager at a football club, and I sit at press conferences wanting to talk about football.
"We addressed that matter, we did everything we needed to do, it's time we moved on."
He had previously expressed the club's wish that fans be "respectful" during any tributes.
There were also disruptions to tributes at some of Saturday's Premiership fixtures.
A minute's silence at Ibrox was disrupted by some Dundee United supporters.
Boos and derogatory chants could be heard coming from the corner of the stadium housing several hundred United supporters before Rangers played God Save the King.
In a brief statement, Dundee United later stated that they had "reached out to advise our supporters of the pre-match arrangements with the expectation that the minute silence would be observed".
Prince Andrew pays tribute to the Queen: 'I will forever hold you close to my heart'
'I love the history of pageantry': The royal superfans who have been camped on The Mall
Archbishop of Canterbury praises King Charles ahead of preaching the sermon at Queen's funeral
There were similar reactions ahead of Hibernian's game with Aberdeen at Easter Road, where boos and chants were audible during a minute's applause.
The Scottish Football Association had postponed all matches the previous weekend following the Queen's death and gave clubs the option of choosing whether and how to pay respects when games resumed.
In a joint statement with the Scottish Professional Football League last Monday, the SFA said: "This week, as a mark of respect and in keeping with the period of national mourning, home clubs may wish to hold a period of silence and/or play the national anthem just ahead of kick-off, and players may wish to wear black armbands."