Klopp's incendiary comments came after seeing Dortmund crash out of the DFB Pokal in a 1-0 loss to the Bavarians thanks to Arjen Robben's first-half strike.
"At the moment, it's a bit like what the Chinese do with industry. They look at what the others are doing and imitate it, but with more money and different players," the 45-year-old said.
Heynckes retaliated: "It's very important to show dignity in victory, and especially in defeat."
Klopp has since backtracked on his initial remarks and, speaking after the club's 3-1 win over Hannover, appeared to offer his apologies.
"The last thing I want is to criticise a renowned colleague," he told WDR2-Radio.
"Jupp Heynckes is an excellent coach. If needs be, I will gladly apologise. So, Jupp, if you can hear me, I'm sorry."
Borussia Dortmund sit second in the Bundesliga after victory against Hannover with 46 points from 24 games, though still 14 points behind league leaders Bayern.