Los Blancos were dire in the first half, conceding three goals before the break as they were ran ragged by the Ukrainian side, who found the back of the net via Tete, Manor Solomon, and a Raphael Varane own goal.
The hosts improved in the second period and scored two before the hour mark, setting the stage for a potential momentous comeback.
However, Shakhtar stayed strong to claim all three points and a famous away win.
In terms of blame, the buck stops with ZIdane, according to the man himself.
"I did not see the team as I wanted and when you do not see the team as you wanted it is your fault," the Frenchman said following the defeat.
"It's a bad game, a bad night. I'm the coach and it's up to me to find the solution.
"We deserve the criticism, all of us, and me first. Luckily we had a reaction in the second half because they don't deserve that, they are champions and it bothers me.
"I am responsible and I have to look for solutions because that cannot happen."
The defeat against Shakhtar comes just a few days after Madrid suffering a shock loss versus Cadiz in La Liga.
This weekend, they face Barcelona in the Clasico.