Los Blancos needed to avoid a defeat against the Reds in England in order to book a date with Chelsea in the last four.
Real Madrid were resolute and compact as they kept a clean sheet against Jurgen Klopp’s men.
"It was known that we were going to suffer and we expected a very strong Liverpool in the first 15 minutes,” Zidane told the media after the game.
“This is normal, they are the quarterfinals of the Champions League. But in the end we are classified and very happy.
"We are all together and the team is always there and wants more. We have not won anything, but we are alive in both competitions."
"We deserved to pass the tie and I am happy for all the boys. Emotionally it gives us a lot of strength.”
Zidane was asked about Real Madrid’s next game in the Champions League against Chelsea, but the French coach said his men have to rest and reflect before thinking about the Blues.
He added: "Let's enjoy a little first and rest a little, because we still have games before. We know that Chelsea is a very good team."
Next up for Zidane and Real Madrid is a trip to Coliseum Alfonso Pérez to face Getafe in La Liga on Sunday.
