Raul Garcia's first-half double was enough to knock the holders out and end their nine-match unbeaten run at La Rosaleda on Thursday.
Karim Benzema's 13th goal of the season gave Los Blancos hope after Marco Asensio hit the woodwork twice, but the Basque side held on to secure only a second win over the LaLiga champions in 23 matches and a first victory under new coach Marcelino.
Madrid boss Zidane felt his side fell short of the high standards he expects in the first half, but he will not be dwelling on the setback.
He said: "Our first half was difficult, we didn't get into the game well, they scored two goals. They had two chances and two goals. When you are two goals down it is always difficult.