Bayern, who take on Chelsea in the Champions League final next weekend, were torn apart by the Bundesliga champions on Saturday night as they competed a domestic double.
"We can have no complaints. We just did not start with any concentration," said Heynckes.
"It started as early as the third minute, our defensive performance was catastrophic and we did not deserve to win.
"The players are disappointed today, but we have a big goal in front of us next Saturday and then I hope that we will have got over this shock."
Bayern's honorary president Franz Beckenbauer claimed the club could forget about winning the Champions League if they played as badly against Chelsea.
"I never expected Bayern to commit so many mistakes," he told Sky television.
"Dortmund took advantage of Bayern's mistakes. It was an embarrassing defeat.
"There is still a chance, but if they play like they did today, then they are not going to win the Champions League."
Dortmund coach Jurgen Klopp hailed the win which sealed the club's first league and cup double.
"This was a dream final for Dortmund," he said. "We were amazing and struck at the decisive moments.
"Words really cannot describe what is happening here."
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