Mandzukic, who scored the first goal but will now be suspended after picking up a yellow card, said that he and his teammates wanted to remain patient in order to pick off Juve.
"No, it wasn't easy," UEFA.com quotes Mandzukic as saying. "We knew we were preparing for a tough game. We said that we had to keep our cool and try to get a goal, and that's what we did.
"We were ready for them to come at us. We didn't think that it was going to be easy after winning 2-0 in the first leg, like people were thinking, but after a good period from Juve, we got back into the game and it was easier for us.
"I think it was the 65th minute [when I scored] and we knew then that they had to get four goals, so that made it easier for us."
Bayern have gone into the draw for the semi-finals, which takes place on Friday.