Real beat Bayern Munich 1-0 in the second leg of the first knockout round at the Bernabeu to clinch a 2-1 aggregate victory and reach the last eight.
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"I'd have loved to see them go through," Beckham told reporters after Wednesday's game. "I'd have loved to have played them."
"I watched the game and there's no more that the players could have done to go through and as a Manchester United player I was involved in a lot of games when we beat teams right at the end."
"I'm disappointed, obviously, as a Manchester United fan and a Real Madrid player."
Real have a six-point lead at the top of the Primera Liga and are looking forward to a King's Cup final appearance against Real Zaragoza on March 17 but Beckham played down talk of a treble.
"Everyone else is talking about it except the players and the people at the club," the England captain said.
"We're taking each game as it comes and hopefully we'll just keep on winning them."
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