The German side repeated their 2-0 first leg win and became the first overseas side to win in Turin since the new stadium was built two years ago.
And after securing the Bundesliga title last weekend, coach Jupp Heynckes now wants to prove they are the best side in Europe.
He said: "In the last weeks there's been a lot of praise but the positive thing is the team has not been influenced by this. Too much praise is not good.
"We are champions and that was our aim but we also have other aims. We now have to see if we are on par with Real and Barcelona."
Croatian striker Mario Mandzukic, who scored the first goal in the Juventus Stadium said they had produced a great performance.
He said: "It was decisive that we played like we did in Munich. It was a great atmosphere. It was not easy and we had to stay patient.
"I am happy to have scored but happier that we are through. But we are not yet done."