Celtic will not appeal against the £12,700 Uefa fine for "illicit chanting" by some of their fans in the home Europa League game against Rennes.
Uefa's control and disciplinary body announced its decision on Monday.
Celtic chief executive Peter Lawwell said: "The heavy fine imposed by Uefa is an indication of the seriousness with which it treats such matters.
"We reiterate our position that, however small the minority, such chanting is not welcome at Celtic."
The fine was in reaction to a report by the Strathclyde Police match commander to the Uefa delegate of instances of some fans "singing offensive songs" during the 3 November fixture.
"Clearly, it is very disappointing and a source of real regret amongst our supporters that Celtic's proud history of exemplary conduct has been tarnished in this way by such a tiny minority," Lawwell said.
"However, this is a clear warning that such behaviour will not be tolerated and, together, Celtic Football Club and our supporters will do all we can to ensure that this incident is not repeated.
"We would like to thank our supporters for their magnificent conduct since the match against Rennes."
"We are proud of the fantastic and positive reputation we have established across Europe over many years, and the club and our fans will be doing all we can to ensure that this is protected."
At the club's annual meeting in October, Lawwell urged fans to refrain from singing pro-IRA chants.
He said that the club had been "inundated" with complaints from their own supporters following their 2-0 defeat by Hearts at Tynecastle.
Last Monday, the Scottish Premier League announced it would take no action against Celtic after deciding the club had taken "all reasonably practicable steps" to prevent offensive chanting in their home match against Hibernian on 29 October.
Rangers were fined £13,300 and "severely warned" by Uefa when the conduct of their supporters first drew the attention of Uefa in 2006.
Uefa had originally found Rangers fans not guilty of disciminatory chants at the Champions League tie with Villarreal but that decision was overturned when challenged by disciplinary inspector Gerhard Kapl.