Luka Modric's fantastic 85th-minute strike ensured a fourth win in Zidane's first five games as head coach.
Real are in third place, four points behind Barcelona, having played a game more than the Catalan side.
"We are going to try to improve everything - at the back and in attack because we need to score more goals," Zidane said.
"We had a lot of chances and we know that at this level we need to put them in in order to be a bit more relaxed in our play."
Meanwhile, right-back Dani Carvajal, who assisted Karim Benzema's opening goal, said they are still in the title race.
"Modric's goal allows us to stay in the hunt for La Liga and fight until the end," he said.
"Until it is mathematically impossible, we are going to give everything. We are going to take it game by game, which is ultimately what will lead us to titles."
Real Madrid boss Zinedine Zidane said his team "have to improve everything" after their late 2-1 win over Granada.