Casillas could only watch in despair as Lionel Messi's superb volley sealed a 3-2 win at the Nou Camp to allow the Catalans to lift the trophy 5-4 on aggregate.
With the scores level at 2-2 from the first leg in Madrid, Barca took the lead twice on Wednesday only to be pegged back both times - first through Cristiano Ronaldo and then Karim Benzema's effort eight minutes from time.
However, Messi popped up with the winner with just two minutes left in the game and soon after that both sets of players and their benches were involved in an ugly brawl.
"Based on the chances created, the fairest thing would be a draw," Casillas said in a post-match interview.
"In a match like this, there are many interests and of course a conflict can arise."
Barca were angered by a late challenge on new signing Cesc Fabregas by Marcelo near the touchline. The incident sparked heated confrontations between the players and coaching staff of both teams but Casillas feels it was simply a case of Barca overreacting once again.
"Marcelo committed a foul and they [Barcelona's players] threw themselves to the ground, like always," he said.
Meanwhile, the slanging match continued after the game when Barca coach Pep Guardiola hit out at the behavior of his opposite number Jose Mourinho.
The Madrid coach was seen poking Guardiola's assistant, Tito Vilanova in the eye during the mass brawl between the two teams.
"The images speak for themselves," Guardiola said.
"There are things that should not happen in football [and this is one].
"This could end badly if unchecked. I can do something with my players, and make sure that they behave their best, but I do not give lessons to anyone [else]."
Mourinho also appeared to blow Vilanova a kiss after he was pushed away for pinching him.