Dortmund coach Jurgen Klopp was recently critical of Bayern, saying that their director of sport Matthias Sammer "should thank God every day" for being given the opportunity to work with the Bavarian club.
"That sentence shocked me at first, and then it angered me," Rummenigge told the Welt am Sonntag newspaper.
"Matthias won the Champions League as a player with Dortmund, and then he coached them to the Bundesliga title.
"Bayern would never permit themselves so say anything about somebody in Dortmund who used to be with us and is now with them.
"We're at a level which reminds me of the relationship between Barcelona and Real Madrid. We need to return to a level of decency."
The transfers of Mario Gotze and Robert Lewandowski to Bayern have been one of the main causes for Dortmund's ill-feeling towards their rivals, but Rummenigge insists his club have not willingly tried to hurt their opponents.
"It's not like we sign players from Dortmund or Schalke to hurt other clubs," he said.
"We only sign players who will give Bayern more quality immediately."
Meanwhile, Bayern midfielder Xherdan Shaqiri has stressed he is happy at the club as rumours persist about him leaving this summer.
Several Italian sides have been linked with the Swiss midfielder, whose brother says he is unhappy with Pep Guardiola's rotation policy which is limiting his appearances this season.
However, Shaqiri says his brother's comments were misinterpreted and that he is not thinking about a move - although he is ruling it out either.
"I never said I want to leave," the former Basle man said. "I'm very happy in Munich and I'm not thinking about leaving.
"My brother's opinion was written a bit differently to what he actually said. But, of course, if a top club comes in, then you've got to consider it, but every player is like that."
The 22-year-old came on for the final 17 minutes of Bayern's 2-0 win in Mainz on Saturday, making his 15th appearance of the campaign. Only eight of those appearances have come in the starting XI.