Barcelona ran out 3-0 winners at the Santiago Bernabeu on Saturday, sweeping Madrid aside thanks to second-half goals from Luis Suarez, Lionel Messi and Aleix Vidal.
Madrid, who had Dani Carvajal sent off just before Barca's second goal, now trail the Catalans by 14 points in La Liga, leaving them with a mountain to climb if they are to retain their title.
Yet, although Zidane accepts the loss was "painful", he does not think Madrid are in crisis.
"We are not playing badly, that's why it is even more painful," Zidane said in a news conference.
"Football can change so quickly. Many people said they [Barcelona] were bad in pre-season, and now we will be labelled as bad tomorrow [Sunday].
"This is football, we have to accept it. When you win, [people think] everything is wonderful and when you lose, everything is f***** up.
"We are sad because it is a painful defeat, but, at the same time, we will not give up - that's for sure.
"What we have to do now is to rest as much as possible. We do have a week off and we will be back stronger than before.
"Real Madrid never surrender, whatever happens."
Zidane also defended his decision to leave Isco on the bench after deciding to start with Mateo Kovacic, with the aim of limiting Messi's influence on the match.
"I have to make decisions. The idea was to keep an eye on Messi, and Mateo did well. We made a decision and that's it," the Frenchman told beIN SPORTS, before further discussing the issue in his post-match media conference.
"I'm making decisions as a coach. The decision was Kovacic on the pitch and Isco on the bench at the start. Then, because of how the match went, I was not able to use Isco.
"I had to use Nacho [Fernandez] because of the red card and had two changes left with one player less. That changes the game.
"I'm the coach and it's always going to be like that while I'm here.
"I will not regret anything. If you score in the first half the match is different. I know I will take the criticism, but that's football, and it will not change how I think.
"I make these decisions and I accept what happens."