Atletico remain in the box seat to clinch their first LaLiga title since 2013-14, but Zidane's side remain in the hunt should there be any slip-ups.
"We'll keep going; there are two games left and we'll go to the end, until the final minute, we'll give it our all," Zidane said post-game, DPA reports.
Atletico's final two league games are at home to 11th-placed Osasuna and away to 18th-placed Valladolid, while Real go to ninth-placed Athletic Bilbao and host seventh-placed Villarreal on the final day.
Los Blancos are unbeaten in their last 16 games in La Liga of which they have won 11, the best current unbeaten run in the competition. In addition, they have equalled their best unbeaten run in a single league campaign under Zidane, achieved in 2016-17.
"The only thing we can keep doing is chasing Atletico and hope they don't win," goalkeeper Thibaut Courtois said.
"We have to make sure they don't have any margin for error. They won and all we can do is look at ourselves, and focus on the difficult game at Athletic Bilbao, which is another final."