"We're through to the semi-finals after beating a great team, strong opponents," the club's official website quotes Heynckes as saying.
"We expected Juve to apply pressure at the start. We gave away the ball too often and we weren't well organised in defence, which is why we ran into trouble from time to time. But little by little we took control of the game.
"We showed all our class in the second half, when we never looked in trouble, so it's a deserved victory."
The draw for the last four takes place on Friday.