Mourinho, as he was in both England and Italy, has quickly become a contentious figure in Spain and under his watch last season Real had four men sent off in five games against their bitter rivals Barcelona.
Barca took the silverware on Wednesday night as a Lionel Messi brace secured a late 3-2 victory but there was still time for another Real red card as a brutal challenge from Marcelo saw him dismissed in the closing moments.
A huge melee unfolded involving players, substitutes and staff from both sides, with Mesut Ozil and David Villa both shown red despite having already been substituted.
Mourinho, meanwhile, may come under scrutiny for his role in the fracas as he was pictured heading towards Barca coach Tito Vilanova and making contact with his face.
Vilanova responded by pushing Mourinho, who walked away grinning.
After the game, Pique fumed at the Portuguese's actions.
The defender told Marca: "I do not talk about the brawl. But it's a shame, it is not the first time and it's always the same.
"Someone has to take action on the matter. Mourinho is destroying Spanish football. There is talk about the Catalans, but the problem is with Madrid. "
"I think it's going too far. It cannot always end well. In the end this will end very badly."
Mourinho's opposite number Pep Guardiola did not wade into the issue but had a word of caution for those involved in the tense atmosphere on the pitch.
"The images speak for themselves," he told Marca.
"We must be careful, because one day we will cause harm, not on the field but off, and we're all a little responsible for this. "
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