The newly-crowned Bundesliga champions saw off the Serie A champions-elect with consummate ease, displaying the gulf between the two sides which Juve coach Antonio Conte had been so keen to emphasise on the eve of the game.
Goals from Mario Mandzukic and Claudio Pizarro saw Bayern ease through and set up the prospect of an all-German semi-final with Borussia Dortmund.
"We expected Juve to put us under pressure to begin with and we lost the ball too easily and did not have a very good organisation in defence," he said.
"That is why, now and again, we had a few problems.
"But bit by bit we controlled the game and we showed our class in the second half.
"We did not let them have a chance then, which is why this win is deserved."
Despite the margin of victory, Heynckes was quick to pay tribute to the Bianconeri.
"We have made it through to the semi-finals against a great team, a strong side," he added.
"It was really enjoyable to play in such a modern stadium in front of this atmosphere."
Juve coach Antonio Conte returned the compliments, acknowledging Bayern's strength and highlighting the difference between the two sides.
"The best team won," he said. "They proved that in the first leg and confirmed it here.
"They are a side built to win and to say that this is the strongest Bayern of all time would not be ridiculous.
"There is still a big gap between us and Europe's best and we've got to keep on working to bridge it.
"Today, we woke up from this beautiful dream, and now we have to focus on winning the Scudetto."