Second-half Cristiano Ronaldo and James Rodriguez goals gave Madrid a 2-0 win at the Santiago Bernabeu on Tuesday, sending them into the last eight with a 4-0 aggregate triumph.
It could have been very different for Zidane's side, with Mohamed Salah missing two clear-cut chances for the visitors, while Edin Dzeko and Alessandro Florenzi also failed to make the most of good opportunities.
But the Bernabeu boss was thrilled to keep a clean sheet and praised a number of the key performers in his attacking ranks.
"It was a difficult game, but in the end we got our objective which was to go through and we didn't concede a goal," he said.
"Over the 90 minutes many things could have happened because we were up against a team with good and fast footballers. But we got the job done, have achieved our goal and now we are thinking about the next game.
"We are a squad of 26. Casemiro played well, like everyone else, but he was especially good defensively. Lucas Vazquez was also important. He gives everything whenever he plays and he always competes that is a good thing for a coach.
"I am happy with James goal because he is training well and scoring is important for a player like him.
"Every time he is on the pitch, Ronaldo wants to show his best and to score – he did that."
Zidane called for unity after some home supporters whistled at various sections of the match to show their disapproval.
"It is important that the supporters are with the team," he said. "They always want more of their players and players always try to do more."
Real Madrid are back in action with a La Liga game at Las Palmas on Sunday.
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