Rangers have been fined £13,300 for the conduct of their supporters during the Champions League tie with Villarreal.
Rangers fans were in Villarreal in large numbers
Uefa originally found Rangers fans not guilty of disciminatory chants but that decision was challenged by disciplinary inspector Gerhard Kapl.
The governing body had said it could not tackle sectarianism because it was a particularly Scottish social problem.
But Rangers have now been "severely warned" about their responsibility for any future misconduct of their fans.
Rangers issued a statement saying: "Rangers Football Club is disappointed by the decision by Uefa's appeals body not to uphold the original verdict of the control and disciplinary body.
"The appeals body has concluded that Rangers fans were guilty of discriminatory chanting at both legs of the Champions League matches against Villarreal.
"The club and its legal advisors put forward a strong case highlighting the important intiatives Rangers is taking to tackle sectarianism, racism and other forms of inappropriate behaviour which were complimented by the chairman of the appeals body Michel Wuilleret.
"The decision by Uefa should be seen as a strong warning to the minority of supporters whose inappropriate behaviour brings the club into serious disrepute.
"The controlling authorities in football will be monitoring closely any future misconduct by supporters in relation to sectarian and discriminatory behaviour.
"Rangers Football Club does not intend to take this appeal any further."
Austrian official Kapl, who compiled evidence during Rangers' matches against Villarreal, had recommended a £25,000 fine and the closure of a stand at Ibrox.
Rangers were fined £9,000 after a window on the Villarreal team bus was smashed ahead of the second leg of the Champions League tie in Spain.