The French centre-back himself scored Los Blancos' third goal at Camp Nou as Jose Mourinho's team progressed to the final 4-2 on aggregate.
"We are happy and when we play like that, as a team, we know we can win," he told Madrid's official website. "Now we have to move forward and think about the final and our next matches.
"Barcelona are a difficult team to defend against because they have very fast players, so we played tight together and tried not to leave spaces.
"I try to improve and learn, that is good for my career. I'm ready to play and to help the team and that is what I am here for."
Varane joined Madrid from Lens in 2011.