The goals were the only shots on target at either end, although Villarreal had 13 total attempts to Madrid's six. Zidane still felt his team deserved the points.
"I think we deserved more, considering what we did," he said. "Especially in the first half. We've dropped two points.
"I'm upset for the players because of the effort they gave. I felt we could have taken the three points today and that's a shame."
Zidane had acknowledged prior to the match that there was pressure at Madrid, but he defended his hopeful outlook despite another tough result.
"I keep looking forward," he said. "You continue with what you are doing and I with my work."
Other questions focused on three of his players: Mariano, who starred in Benzema's place, Eden Hazard, returning after contracting coronavirus, and Isco, appearing only as a 65th-minute substitute.
Mariano played 85 minutes, more than he had across all league matches combined since the start of last season (54), and scored with his only shot while creating two chances for team-mates.
He won three of his eight duels but could not see out the match, Zidane explained.
"The thing about Mariano is that he hadn't played for a long time," the coach said. "He was exhausted."
Hazard's display was slightly less impressive, failing to attempt a shot or play a key pass in over an hour.
"He's there. He played," Zidane said. "We need to manage the minutes well, but he's with us and he's good."
Isco likewise had no say in proceedings in an attacking sense and has still made only three LaLiga starts this term as he is linked with a January departure.
"What is happening inside will stay inside," his coach said. "Right now, Isco is a Real Madrid player and is with us. There's nothing to talk about."