But instead of bouncing back they proceeded to fold in the face of a relentless Ajax team that exuded the youthful energy Real are so badly lacking.
Bale joined Real from Tottenham in 2013 for £85m and has won four Champions Leagues and one La Liga title with the Spanish club.
In the end, the club renowned for assembling its team with expensive "Galactico" signings was undone by a club centered around a core of homegrown young talents.
DF Sergio Reguilon, 5 - The most trying night of his first season as a Madrid first-teamer - as Ajax's super mobile front three regularly opened up spaces down his side.
Santiago Solari is now in charge of the Champions League holders, after Julen Lopetegui was sacked earlier this season.
Real Madrid are the first reigning Champions League winners to fail to qualify for the quarter-final stage since Chelsea in 2012-13 (knocked out in the group stage). Madrid had reached at least the semifinals in eight straight seasons and hadn't failed to make it past the last 16 since 2010.
Neres added a goal in the 18th minute to double the lead after finishing off a spectacular play from Dusan Tadic.
"Of course we miss Cristiano", Luka Modric said.
Vinicius Junior was hurt at the end of a long run in which he almost opened the scoring for Madrid.
DF Raphael Varane, 6 - Things might have been different if his fourth-minute header had hit the net instead of Ajax's crossbar. Asensio and Nacho Fernandez also wasted opportunities as Madrid's lack of scoring touch was costly again.
Real did have chances throughout the second half but couldn't find the killer pass or finish to get back into the game and Ajax kept plugging away.
That was emphasised when Ajax scored their third, a sensational shot into the top corner from Tadic, his sixth goal of the competition.
After allowing a goal, Ajax struck back in two minutes. with Lasse Schone beating Thibaut Courtois on a free kick.