Marcelo struck the winning goal in the 86th minute after Dani Parejo had cancelled out a Cristiano Ronaldo header, set up by a sublime Carvajal cross.
Speaking afterwards, Zidane was full of praise for his side's unlikely heroes as Madrid snatched yet another late result to move three points clear of Barcelona at the top of LaLiga.
"I'd like to secure the result earlier but we know we can score at any time and with any player," he said.
"Marcelo and Dani's performances were very good. They attacked a lot. They are among the top three or four full-backs in the world.
"When you don't get the second goal, they [Valencia] can always score, but the result is deserved. We worked hard and put in a lot of energy."
Zidane felt Valencia's defensive gameplan made life difficult but conceded that Madrid should have made the most of their chances, with Ronaldo seeing a penalty saved by Diego Alves and Karim Benzema hitting the post.
"It's worse and even more so when it's against us," he said of the visitors' approach. "But there are no excuses. They played their game and we made it difficult by not scoring the second. We had a lot of chances; that means we can improve.
"The fans knew we needed a push and they responded in the best way. The fans helped us to get the second. That's what this club has."
Isco was surprisingly left on the bench but Zidane confirmed that he will play some part in Tuesday's Champions League semi-final first leg against Atletico Madrid, while Raphael Varane could also return.
"You'll see him on Tuesday," he said of Isco, who has three goals and one assist from his last two league appearances. "It's true that he's playing really well but he played at the Riazor [against Deportivo La Coruna on Wednesday]. I have to think about the group.
"Varane will be available on Tuesday but we have to be careful. The last time he came back he got injured and I don't want that to happen again. There are a lot of important games left."