The Bavarians were routed 5-0 on aggregate in the semi-finals by the eventual champions of Europe but the club CEO feels that the Catalan knows what went wrong
The Bavarians were heavily fancied to become the first side to successfully retain the trophy but their hopes were obliterated by Los Blancos, who hammered the Bundesliga champions 5-0 on aggregate in the semi-finals.
Rummenigge believes that Bayern were punished for easing up in the Bundesliga after clinching the title with a record seven rounds remaining and does not think that Guardiola will allow his players to suffer from the same sense of complacency next season.
"[The Madrid loss] is not forgotten, particularly as far as Pep is concerned," the FCB CEO told his club's official website.
"We paid the price that night for taking our foot off the gas in the league. But the defeat taught us a lesson or two.
"I think it's incredible and admirable the way Pep stood up immediately and took full responsibility for the result. That's not a given in modern football."
Rummenigge, therefore, believes that Guardiola's first campaign at the helm should be considered a great success given Bayern not only won the league but also the DFB-Pokal.
"I think we can look back on an excellent rather than just satisfactory season," he reasoned.
"You’d expect the season following a treble to be very difficult. You're slightly short in terms of motivation, commitment and determination.
"But it was quite the opposite for us last term as there was no dip in performance levels.
"The players, and the coaching staff in particular, have been brilliant. Pep set out a new approach. He has demanded more of the players, supported them and changed the way we play quite a bit.
"It's thanks to him that we avoided a dip in form."
However, while Rummenigge has been delighted with the 2013-14 campaign overall, he called on a couple of players to up their performance level next season.
"The whole squad has done brilliantly," he stated. "Several players have been outstanding. Arjen [Robben] has had a sensational season, simply world-class. Philipp [Lahm] was impressive again, Manu [Neuer] an absolute safe pair of hands in goal.
"But there are a couple of players who need to up their performances a bit next season."