Madrid made light work of its visitor despite initially looking a little shaky at the back, with Legia netting its first Champions League goal in 21 years to bring the score back to 2-1.
Zidane's men ultimately had little difficulty in dispatching its opposition, as Gareth Bale, a Tomasz Jodlowiec own-goal, Marco Asensio, Lucas Vazquez and Alvaro Morata did the damage.
But there was to be no Ronaldo goal, as he saw numerous opportunities wasted in the second half.
"Everyone wants Cristiano to score three, four, five goals," Zidane said. "He had many chances tonight, [but] he scored on Saturday (local time) and will score next weekend.
"We all expect more from Cristiano and he knows that. We want him to score three or four.
"There was no goal today but he got two assists and I also like that."
Assessing the overall performance, Zidane believes his side have defensive improvements to make.
"I'm happy with the result, with goals," he said. "It is clear that we can improve.
"Defensively the balance of the team was not perfect sometimes, but our choice was to play offensively. Though we have risked and have given chances to the opposition.
"The important thing is to score and win and that's what we have done."