After an impressive opening to the contest, the Reds were handed a huge blow to their aspirations as Mohamed Salah was forced from the field after just 30 minutes. The top-scorer failed to recover from a shoulder injury picked up in an earlier challenge with Sergio Ramos.
Jürgen Klopp?s side fell behind just after half-time when Loris Karius?s attempt to bowl the ball out of his hands struck Karim Benzema?s outstretched boot and rolled over the line.
Sadio Mane provided hope when he prodded in from Dejan Lovren?s header corner on 54 minutes. However, substitute Gareth Bale put Real back in front with a spectacular scissor kick.
Mane then struck the base of the post to almost level up the scoreline once more, but Bale sealed the trophy for the Spanish side for a third successive season when Karius failed to keep out his long-range effort.