The defeat meant the champions had picked up just one point from their opening two games.
“Real was very bad, an unacceptable match,” said Mourinho afterwards.
“The only message I want you to take away tonight is that it was a deserved defeat for us.
“This was a match in which the defeat was absolutely deserved. More than two matches with just one point it was a horrible match.”
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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.