Lionel Messi scored a late volley to seal a 5-4 aggregate victory over Real in a pulsating encounter that saw red cards shown to three players after tempers boiled over at the end resulting in a mass brawl.
"Mourinho is wrecking Spanish football," Pique told reporters. "People are looking for culprits but they are in Madrid. Someone needs to get the video, analyze it and say who is to blame."
A bad-tempered run of five 'clasicos' last season has seen the heated rivalry between the clubs grew ever more acrimonious.
Mourinho, who was punished by UEFA following his actions after the Champions League semi-final against Barca, accused Barcelona of play-acting to influence referees while their arch-rivals countered that Real were overly aggressive.
"We hope that on Thursday everyone will be talking about a great game of football and not the melee," added Pique, a World Cup winner with Spain.
"It isn't the first time this has happened ... it is always the same people. Someone needs to sort this out."
Real defender Marcelo's lunging tackle on substitute Cesc Fabregas in the final minute of the game had players and both benches jostling and arguing.
Marcelo and Real team mate Mesut Ozil were sent off, as was Barca's David Villa.
HIDING THE BALLS?
In the post-match news conference, Mourinho accused Barca players of going to ground easily.
"Marcelo got a red card because we all know what happens after tackles in certain areas of the pitch," the Portuguese said.
"It was a spectacular game from the first to last minute. But from the first minute of the second half, and I don't criticise it because I know people do it, the ballboys hid the balls.
"It happens with small teams when they find themselves in difficulties."
During the melee of players and management staff, television pictures appeared to show Mourinho sneak up behind Barcelona assistant coach Tito Vilanova and poke him in the eye.
When asked about the incident, Mourinho replied: "I have been polite and played like a man and not fallen to the ground at the first touch. I don't know who Vilanova is."
Barca coach Pep Guardiola told reporters: "The images will speak for themselves. This is going to end up badly if it isn't stopped soon."
