Zidane, 20, was afforded his first start for Real ahead of experienced international keepers Thibaut Courtois and Keylor Navas and conceded twice during an entertaining league clash on Saturday.
Questions were immediately raised after he conceded the first goal in the opening three minutes but his father is adamant that his place in the team was merited on effort on the training ground.
"I'm happy for him because it was his debut at the Bernabeu but Luca is strong for the third goalkeeper," he told reporters, as per Marca.
"Thibaut was unfit and we wanted to rest Keylor Navas after being away with his national team. Luca has been in the lower categories at Real Madrid for 16 years but he has quality and personality.
"It was a crazy game, a nice one to watch. We can play much better but we are happy with the victory and the effort."
While Zidane shocked Los Blancos supporters with his heavily rotated squad selection, he conceded it wasn't something he planned on doing.
"I am just trying to win all of the games but after the international break, I always try to rest players and there have been players who have been working here for 15 days," Zidane explained.
"I don't believe in the formula that you can win titles with eleven men and in a 60-game season, it is impossible to win with 11.
"That's my way of thinking and I just try to pick the best team possible. People can think that I want to please everyone but that isn't the case."