Lionel Messi scored twice after Real had midfielder Pepe sent off in the 62nd minute, giving the Catalans a 2-0 first-leg lead ahead of next Tuesday's return at the Nou Camp.
Mourinho was sent to the stands for protesting the red card decision.
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"In the post-match press conference, Jose Mourinho severely criticised the referee, Wolfgang Stark, and insinuated that UEFA treated Barca favourably," Barca said in a statement on their website.
"The club's legal department are now studying whether to take his remarks to the UEFA disciplinary Commission.
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"The Real Madrid manager said: 'Josep Guardiola is a fantastic football coach, but he has won one Champions League which would embarrass me after the scandalous goings on at Stamford Bridge (in 2009), and this year if he wins it again it will be after the scandalous goings on at the Bernabeu'.
"Mourinho also claimed: 'I don't know if it's the UNICEF publicity or the friendship of Villar at UEFA, where he is vice president, I don't know if it's because they are so nice, but they have got great power. The rest of us have no chance'."
Barca backed the re-election of Angel Maria Villar to the presidency of the Spanish soccer federation, while Real backed a rival candidate.
UEFA said it was waiting for reports from the referee and match delegate before announcing whether any disciplinary cases would be opened.
UEFA added that its regulations clearly stated that any player or official shown a red card in the technical area or pitch would be automatically suspended from the next European match.
