The European champions drew 2-2 at the Nou Camp to knock holders Real out at the quarter-final stage 4-3 on aggregate on Wednesday, after a match full of disputed refereeing decisions.
Spain midfielder Xavi was caught on camera speaking to Barcelona Television before a scheduled interview was due to start.
"They're the pits, they don't know how to lose," said Xavi shaking his head, on a video clip released on the El Mundo website.
Xavi's Spain team-mate, Real defender Sergio Ramos, was sent off for a second bookable offence near the end on Wednesday for catching Barca midfielder Sergio Busquets in the face with his arm as the two jumped for a header.
Ramos used his official Twitter account to accuse Busquets, another Spanish World-Cup winning colleague, of feigning injury.
"I'm pleased the club [Real] are going to appeal my second yellow card because although some don't stop rolling around all over the place, I didn't touch him," Ramos wrote.
The lingering bad feeling after the recent 'Clasico' threatens to disrupt the harmony of the Spanish national team like last year, when the internationals from both clubs were reported to have spoken to each other privately to defuse the tension.
A photo of Real coach Jose Mourinho standing by referee Fernando Teixeira Vitienes's car after Wednesday's game has also been in the media, with Barcelona-based daily Mundo Deportivo reporting he harangued the match official.
"What an artist, you like to mess up the work of serious professionals," he was quoted as saying. "Now go and smoke a cigar and have a laugh, you have no shame."
Mourinho's spokesman Eladio Parames confirmed what the Portuguese had said on his official Twitter account.
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