Madrid lost the first leg 2-0 and went behind to a Pedro goal nine minutes into the second half at the Camp Nou, before Marcelo gave Jose Mourinho’s men hope of a recovery.
That never came as Barca cruised to their third Champions League final in six years with a 3-1 aggregate win.
But Madrid have pointed to an incident early in the second half, when Gonzalo Higuain netted only to see his effort chalked off as play was stopped only moments earlier.
Cristiano Ronaldo accidentally tripped up Javier Mascherano in the lead-up play, although the Portugal international appeared to have himself been tripped by a home defender to initiate the contact.
“(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.’’
Mourinho, like Pepe, was banned following his own red card in last Wednesday’s ill-tempered first leg and, unable to communicate with the Madrid bench during the game, the Portuguese chose to stay away from the stadium.
“We couldn’t have any communication with him, but we talked about the game beforehand and the changes we could make,” Karanka said.
Real Madrid midfielder Xabi Alonso claimed the performance of the referees cost them a place in the final.
Higuain’s disallowed goal was one of the major talking points surrounding the officials and Alonso said the whole Madrid team were upset with what they perceived to be poor decisions.
“When we scored the first goal it would have been totally different and we feel so many bad decisions have been made against us and we are not happy about that,” he said.
“We think we did a good job but decisions went against us, we really feel that way.”
Barcelona boss Pep Guardiola did not agree with Alonso’s opinions on the refereeing of both legs, insisting it was not the main talking point.
“I don’t have time for that, it has been a tough 20 days and we have played the richest team in the world many times, the referee may have had an influence but we were very good in the second match,” he said.
Guardiola also said he was happy to be returning to the venue where the club won their first European Cup 19 years ago.
“Football is coming home so it an honour to play at Wembley,” he said.
“We won our first Champions League in 1992 at the old Wembley and we are ever so proud for our club and players.”
The 40-year-old Barca manager thinks Manchester United will progress against Schalke to set up a repeat of the 2009 final which his side won 2-0, but he believes that would have no bearing on any potential rematch.
“I suppose it will be Manchester [in the final], it was two years ago and I think Alex Ferguson will always be there so for us it is an honour and for me as a young coach it is an honour to arrive at the final and play them,” he said.
Subs for Barcelona: Keita for Villa 74, Afellay for Pedro 90, Abidal for Puyol 90.
Subs for Real Madrid: Adebayor for Higuain 55, Ozil for Kaka 60.