'Los Blancos' were famously knocked out by Leganes at the quarter-final stage. They won the away leg 1-0 but were surprisingly downed 2-1 at the Bernabeu a week later to miss out on away goals.
It summed up a disappointing season domestically for Real but they still have a chance of winning silverware when they take on Liverpool in the final of the Champions League on May 26.
When asked by reporters if his team's campaign would be disastrous if they didn't win in Kiev, Zidane turned to that Copa del Rey exit as his basis.
He said: "There is not failure here. My failure has been a fair moment, after losing the Copa del Rey, because when you win away from home and play in your stadium you have to go through".
"It was very difficult to take, but there are seasons in which Real Madrid want to win everything, but they can't.
"The important thing is to put hope, delivery, all the desire in the day to day. If you do this, failure doesn't exist".