After Ansu Fati cancelled out Federico Valverde's opener, Sergio Ramos scored a 63rd-minute penalty and Luka Modric sealed Madrid's win at Camp Nou.
Zidane was under pressure at the helm after back-to-back losses to Cadiz and Shakhtar Donetsk, but Madrid moved top of LaLiga after Saturday's win.
And the Real Madrid coach said he had no interest in trying to respond to critics.
"That's not what we're here for, to shut them up," Zidane told a news conference.
"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."
Ramos' controversial penalty proved crucial for Madrid and the defender has now scored each of his past 25 spot-kicks, including shoot-outs, for his club and Spain.
Madrid's overall performance, though, pleased Zidane, as they made it four wins in six league games this season.
"We played a good game, playing against a team that we know is open, that played well," he said.
"I'm happy for the players because in the end it's about that, after the last few days of everything they said. I am happy for them and also to finish with Modric's goal.
"I've seen the team together. I am happy because they're the ones fighting on the pitch. We can enjoy what we did."
Madrid visit Borussia Monchengladbach in the Champions League on Tuesday before hosting Huesca four days later.