Los Merengues conceded twice in the first 10 minutes of the game as Simone Zaza and Fabian Orellana both scored. Cristiano Ronaldo pulled one back just before the break, but Real couldn't find the equaliser.
The result sees Madrid's lead at the top of La Liga shrink to one point, however, they still have a game in hand on second-placed Barcelona.
"The truth is we lost the game in the first 10 minutes," Zidane told a press conference.
"We started well with the ball, playing football, had a chance to score. But we made mistakes at the back, they had players between the lines all the time, and they scored two goals. We were very open, and they punished us.
"Then we had 80 minutes to come back into the game. We had chances to do that, but we lacked many things today. There was a chance to pick up points, which we did not do.
"We did not do badly with the ball, on the contrary, we did well," he added. "Maybe we lacked a bit of cleverness in the final pass, but that's it. They defended very deep, together, were better than us in the air, and that's that."