Gonzalo Higuain was controversially denied a goal in the 1-1 draw at the Nou Camp.
Karanka claimed the performance of the officials proved his side had no chance of making it through to the Champions League final.
"(Jose) Mourinho was right," Karanka said.
"He said that it would be impossible for us to go through. Tonight proved that it was impossible and 100 million people saw it - there is nothing more to add."
Madrid goalkeeper Iker Casillas, who kept his side in the game with a string of fine saves in the first half, was also frustrated at the decision to disallow Higuain's strike.
"It has happened again - just like always," he said after the game.
"Playing 11 against 11 we have shown we can compete without complexes and it takes me back to the first game; if we had finished 0-0 (the score before Pepe was sent off), tonight's 1-1 would have taken us through to the final."