Substitutes Dentinho and Manor Solomon scored in the second half, as Los Blancos were beaten for the second time by the Ukrainians.
Zidane’s men lost 3-2 in the reverse fixture at home in October.
The result in Kiev put Shakhtar level on points with Madrid.
The final matchday on December 9 sees Madrid welcome group leaders Monchengladbach, and Shakhtar travel to Inter.
“No. Not at all. I won’t resign,” Zidane said in his postmatch news conference, when asked if he was considering his future.
“We’ll keep going. In the first half we were really good. I think we deserved to score first, that would have changed things. Their goals hurt us a lot.”
Madrid have now lost five of their last 10 matches in all competitions.