Juventus grabbed an early away goal through Mario Mandzukic and the Croatian got his second of the night on the half-hour mark to make it 3-2 to Real Madrid on aggregate.
Bale was starting in place of Karim Benzema alongside Cristiano Ronaldo in a 4-1-2-1-2 but the Welshman failed to influence the game and was hooked at half-time by Zidane in place of Marco Asensio.
Bales disappointing half was summed up when he played attempted a one-two with Dani Carvajal and played the return pass into the Bernabeu crowd instead.
Bales future has been the subject of plenty of speculation in recent months and Madrid are said to be willing to cash in on the Wales international.
Madrid broke the world transfer record to sign him from Tottenham in 2013 and they want to recoup the £87.5million they paid five years ago.
Manchester United have a long-standing interest in the forward but Alexis Sanchezs arrival in January could block a move to Old Trafford.