Los Blancos are well off the pace in La Liga at the midway stage, finding themselves 19 points adrift of leaders Barcelona with a game in hand to play.
The pressure has been building on boss Zidane, but his side picked up a first win in four against Leganes on Thursday night, leaving the Estadio Municipal de Butarque with a slender advantage for the quarter-final second leg thanks to Marco Asensio's 89th-minute goal.
Speaking to reporters after the match, an upbeat Zidane said: "The result is very good for us, keeping a clean sheet and scoring an away goal. We were committed, defended well, had a lot of balance in our play. We found it difficult to play with more adventure.
"But that is normal, as many of these players do not play often. And the second half was much better. We have to get back to winning games, keeping clean sheets.
"This was a step that way. We cannot say we played a great game, but we got an important result in the tie. That is positive. We hope this is a turning point. We wanted to win today, at a difficult place to play. We are happy with the result."
Madrid welcome Deportivo La Coruna to the Bernabeu ahead of facing Leganes in the return fixture next Wednesday.