Bale had been left out of the squad entirely for the derby win over Atletico Madrid last weekend as well as the Copa del Rey defeat to Real Sociedad in midweek, despite being fully fit and available for selection.
The Wales international played over an hour in Real Madrid's 4-1 victory on Sunday before being substituted.
"He is an important player," Zidane said a post-match news conference. "He has shown it. He hasn't played the last three games and he played 70 good minutes defensively.
"Everyone wants us to have a problem with Gareth, but there isn't one. I'm happy with his game. Offensively and defensively he gave everything.
"He was a bit short physically at the end, that's why he came off. We know the player he is and he'll give us a lot until the end of the season."
Madrid went behind early at El Sadar but came back to secure a comprehensive win, with Luka Jovic coming off the bench to wrap up the three points in added time.
Jovic scored only his second league goal in a season where he has struggled for form and confidence.
"I'm happy for him," Zidane added. "He needed it, he's a pure striker and you can say a lot of things, that he is playing well, but if he doesn't score he isn't happy. He has to improve, but I'm happy with his goal."
One absentee was Eden Hazard, who was left out of the squad again as he continues his recovery from a microfracture in his ankle.
He is expected to return for Madrid's La Liga game with Celta Vigo at the Bernabeu next weekend, with a view to being fully fit for their Champions League game with Manchester City later this month.
"It wasn't the right moment today," Zidane said. "He'll need this week, it will be a long one. We'll see next week."