Second-half goals from substitutes Dentinho and Manor Solomon saw Madrid beaten for the second time by the Ukrainians, after they opened their European campaign with a 3-2 home defeat in October.
The final matchday on Dec. 9 sees Madrid host 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, with La Liga defeats to Cadiz, Valencia and Alaves combining with home and away Champions League losses to Shakhtar to leave Zidane under significant pressure.
"We've had complicated moments and we always will," Zidane said. "We're on a bad run of results. That's the reality. But we have to keep going. ... I think we prepared well, we played a great first half. We have one game left and we have to win and think about going through."
Madrid now face a testing run of fixtures, as they go away to top-four contenders Sevilla in La Liga, face Monchengladbach in a must-win Champions League clash, and then face Atletico Madrid in the derby, all in a week.
"I feel strong. I'll give everything, as always, I think the players will too," Zidane said. "The other day [against Alaves] we didn't deserve to win. I think today we played a good game, but that's football. We have to keep our heads up and think about the next game. When you're on a bad run there's no alternative ... we have to show our character and our pride."
While Karim Benzema returned to the team Tuesday night, Madrid are still waiting for captain Sergio Ramos to recover from injury, and Eden Hazard was ruled out for three weeks Monday because of a thigh muscle problem.