Rangers have been fined 19,500 euros (£13,300) after the appeal against the decision to find the club not guilty of discriminatory chanting was partially upheld by UEFA's appeals body.
The Ibrox club have also been 'severely warned about their responsibility for any future misconduct of their supporters in relation to sectarian and discriminatory behaviour'.
The verdict comes after UEFA's control and disciplinary body last month cleared Rangers fans of `discriminatory chanting' during the Champions League clash with Villarreal.
UEFA's match delegate at El Madrigal, Gerhard Kapl, who had lodged the initial complaint, then appealed against the verdict.
A UEFA statement said: 'UEFA's appeals body has today partially upheld the appeal made against the control and disciplinary body's decision concerning Scottish club Rangers FC and their UEFA Champions League first knockout round tie against Villarreal CF.
'UEFA appealed against the decision on April 12 by the UEFA control and disciplinary Body to find Rangers not guilty of alleged discriminatory chants by the club's supporters at both legs of the tie, on February 22 at Ibrox and March 7 at El Madrigal.
'Rangers have been fined 19,500 euros and severely warned about their responsibility for any future misconduct of their supporters in relation to sectarian and discriminatory behaviour.'
Rangers issued a statement to say they were 'disappointed' by the the decision but did not intend to challenge the verdict.
The statement said: 'Rangers Football Club is disappointed by the decision announced earlier today by UEFA's appeals body not to uphold the original verdict of the control and disciplinary body on April 12.
'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 intend to take his appeal any further.'
Rangers were eventually beaten on the away goals rule by the Spanish team after a 3-3 aggregate scoreline.
Kapl was unhappy with the original not guilty verdict with UEFA's control and disciplinary body claiming the chants were 'related to a social problem in Scotland'.
New Rangers manger Paul Le Guen - a Catholic - has vowed to 'preach tolerance' over the issue.