Real went 1-0 down in the opening half-hour of their first leg encounter in the last-16 tie, but rallied back through a Cristiano Ronaldo brace and a late third from Marcelo.
Despite lauding the comeback at the Santiago Bernabéu, Zidane feels Los Blancos can't afford to allow complacency to creep in when the two side's meet for the second-leg in Paris next month.
"This club has 12 European Cups and that means a lot," Zidane said in his post-match press conference, as quoted via the club's website. "This is such a prominent competition and we want to prove time and time again that this club values this.
"We have to turn our attention now to the return leg, that will be entirely different."