After back-to-back losses, Los Blancos managed to claim a 3-1 victory over FC Barcelona at the Camp Nou on Saturday afternoon.
There have been a number of critics of Real in recent weeks, but Zidane says their job is not to silence the critics.
"That's not what we're here for, to shut them up," Zidane said, as per Goal.
"We do our job, believing in what we do, being together when we have to be and that's what we did. We did it as a team, I'm very proud of them.
"When it comes to defending we had a compact block. Then with a rival open like Barca, we've found gaps two or three times and in the end, it's about trying to play a good game as a team and that's what we did."
Scroll through the gallery to see the top 10 goalscorers in El Clasico history
10. Hugo Sanchez (Real Madrid) – 10 goals
9. Luis Suarez (FC Barcelona) – 11 goals
8. Santillana (Real Madrid) – 12 goals
=5. Ferenc Puskas (Real Madrid) – 14 goals
=5. Francisco Gento (Real Madrid) – 14 goals
=5. Cesar (FC Barcelona) – 14 goals
4. Raul Gonzalez (Real Madrid) – 15 goals
=2 Cristiano Ronaldo (Real Madrid) – 18 goals
=2. Alfredo Di Stefano (Real Madrid) – 18 goals
1. Lionel Messi (FC Barcelona) – 26 goals