Madrid were beaten after conceding an early goal scored by Beñat Etxebarria.
Madrid could not force their way back into the game and could be 11 points behind leaders Barcelona if the Catalans beat Levante today.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.