The 2-1 win meant Real reached the quarterfinals 5-1 on aggregate.
Vinicius Jr said afterwards: "A very important match for our confidence because since the beginning of the season we have had many good games, but we haven't controlled as much as we did in this tie. It was a very tough game, against a great team and a great coach.
"They had possession for a long time, but we knew what we had to do: work and take advantage of opportunities. Of course, I missed many, but today I didn't need as much.
"It's an important moment. All the players knew the good matches were coming, and when Madrid plays in this competition, everything changes; the fans change, and the players change. We are ready for what's coming next."
On converting his penalty, the Brazil international also said: "The truth is I said it was for Fede because he had a great first game. I told him to take the first one, but he didn't want to, and I missed.
"Today he gave me all the confidence, as a captain should do. He gave me the confidence, I scored the goal, and I was able to help the team to come away with the win."