The game at the Santiago Bernabeu was Madrid's seventh in a little over three weeks, and Zidane believes a busy schedule was to blame for his side's uninspired performance.
"We started very well and then in the second half we were a little tired because it's normal to be tired after many games," he explained.
"What worries me is that a lot of my players will not rest because they go with their international teams."
Zidane added: "He could have been in the squad, but since he still had trouble, we decided to leave him out.
"He's had a lot of games and he's had a four-month injury and in the end it's a precaution."
Zidane handed a debut to 18-year-old Achraf Hakimi with Dani Carvajal sidelined by a viral pericardium infection, and the boss was fulsome in his praise of the young Moroccan.
"I'm very happy with him," he added.
"It's his first game here at the Bernabeu, and he was spectacular. I'm happy for him and it's a game he will remember for his whole life. He has done very well."
Zidane also confirmed that Carvajal will not meet up with the Spanish squad next week, but did say that his situation was "not serious".