Real Madrid had two penalty shouts on Raphael Varane rejected by the referee and VAR.
Gareth Bale’s second half goal was chalked off following a VAR check, as Ferland Mendy was offside in the build-up.
This was the first goalless encounter between Los Blancos and the Blaugrana since November 2002.
Speaking after the game, the French tactician admitted that the visitors deserved more than a point.
"I'm happy with the game, but we didn't score," the 47-year-old said.
"When you have chances you have to put them in. You have to congratulate the players because they did very well. We played in the opposition stadium.”
"Sometimes you get two or three [goals] and sometimes not. That's football. I'm not happy for the players, because they deserved more.
"The referee and the VAR have not given [the penalties] and I cannot do anything. The game is already over.”
Real Madrid captain Sergio Ramos echoed what Zidane said about VAR, but insists the technology works in both ways and could benefit Madrid one day.
"We have seen them at the break and they look pretty clear, they are both penalties, but it can't be changed anymore," he told reporters
"The VAR is here to help, it's bad luck. Another day it will be our turn to win a penalty and not have it checked."
