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Mourinho issued a statement on Madrid's website on Tuesday, but made a point to direct his words only toward Madrid fans.
"(I) wish to apologise to Madridistas, and only to them, for my attitude in our last game," Mourinho said. "Some people are better adapted to the hypocrisy in football than I am, and they hide their faces and speak in whispers deep inside tunnels.
"I'm not learning to be a hypocrite, and I don't want to."
The Spanish football federation opened disciplinary proceedings against Barcelona and Madrid on Tuesday, six days after Barcelona won the trophy in a match marred by an ugly finale punctuated by Mourinho's actions.
Mourinho walked toward Barcelona assistant coach Tito Vilanova and appeared to poke him in the eye during the onfield melee between both benches.
Under rules 98 and 100 of the federation disciplinary code, the Portuguese coach could be banned between four to 12 games while Vilanova - whose actions are being investigated under articles 111 and 122 - could be sanctioned for four games after retaliating with a push.
Mourinho also sought to dismiss reports in Spain that he may seek to leave the club, after his spokesman Eladio Parames reportedly told Canal Plus TV that "he doesn't feel embraced by the club directors."
Parames subsequently denied the remark and said Mourinho was "happy" at Madrid and looking to see out his deal, which runs to 2014.
Mourinho said his exit was "impossible."
"Only those who don't know me can dream, make up or believe I may leave Real Madrid at this stage," Mourinho said in the statement. "There is no way I'm leaving. No way!"
Mourinho's actions at the Camp Nou seem to have been a result of the obvious tension between the bitter rivals, who have played six times since April.
The altercation came when both benches cleared onto the field following Madrid defender Marcelo's ugly challenge on Cesc Fabregas just before injury time.
Marcelo and team-mate Mesut Ozil and Barcelona striker David Villa were all subsequently shown red cards and were all given one-game bans by the federation on Tuesday.
The clubs have 10 days to present their cases.
Barcelona won the match at the Camp Nou 3-2 and the two-legged series 5-4 for their 10th Supercup.
