The former Hibs player was admonished by the judge when he made a brief appearance at Edinburgh Sheriff Court yesterday but faced no further punishment.
The Celtic striker was filmed singing “Rudi Skacel is a f****** refugee” along with a pub full of his fellow Hibs fans.
The incident happened in April last year before Griffiths attended a Hearts-Hibs derby game at Tynecastle.
In a statement issued by Celtic, Griffiths said: “I made a mistake, I wrongly became involved in this incident and did not fully consider my actions.
“I apologise unreservedly for this.
“I am pleased that the judge felt no further action was required, however this is a matter which I have absolutely learned from.”
Griffiths could now face action from the Scottish Football Association after disciplinary hearings into the pub incident were postponed last year to allow the criminal investigation to conclude.
The Scotland international was accused of three charges by the SFA, including bringing the game into disrepute and not acting in the best interests of football. The 25-year-old was also filmed singing “Hearts are going bust”, which also sparked an alleged SFA rule breach.
In court yesterday, Solicitor Advocate Liam O’Donnell told Sheriff James Scott that his client was pleading guilty to the charge.
Fiscal Depute Faith Miller said police officers were on duty in Roseburn Terrace at around 10am on Sunday, 30 March, before the derby match. A large number of Hibs fans had gathered waiting for the opening of the Roseburn Bar.
Ms Miller said the fans began singing a song about Skacel to the tune of the Beatles’ Yellow Submarine.
The Fiscal told Sheriff Scott it was “a well-known Hibs song” and Griffiths was seen joining in.
Mr O’Donnell said that, in the 18 months since then, his client had not been in trouble.
He added that Griffiths had been fined four weeks wages for being involved in the incident.
Griffiths started his career at Livingston where he made his debut as a 16-year-old. He then moved to Dundee in 2009 for £125,000.
During his five years in the Scottish First Division he earned six player of the month awards. With Dundee in financial trouble, Griffiths moved to Wolves for around £150,000 in January 2011.
Having failed to break into the Wolves first team, he spent the 2011–12 season on loan to then Scottish Premier League club Hibernian.
He moved last season to Premier League champions Celtic.