It was a performance that convinced Rummenigge, who won two European Cups as a player, of Bayern's ability to oust Los Blancos.
"That was a demonstration of the footballing quality we have in the team at the moment," Rummenigge told reporters.
"The team is infused with total belief, and I do believe being a Bayern fan at the moment is like being in paradise.
"We have to keep up our concentration up for the Champions League semi-finals, but if anyone can beat Real Madrid at the moment it's Bayern."
25 - Thomas Müller scored his 25th goal for @FCBayernUS/@FCBayernEN in the @DFB_Pokal (same as Karl-Heinz Rummenigge), only Gerd Müller scored more often (78). Scorer. #B04FCB pic.twitter.com/Q5QXGuQoKR— OptaFranz (@OptaFranz) April 17, 2018
Meanwhile, Rummenigge suggested the war of words between his club and Fredi Bobic was now over, although he could not resist a slight barb at the Eintracht Frankfurt director of football.
Bobic brandished the German giants as "unprofessional" in their approach to and appointment of Frankfurt's Niko Kovac as their new head coach, prompting forceful responses from both Rummenigge and Bayern president Uli Hoeness.
"I think Fredi has seen reason after the admonishing words from Uli and me and has cooled down a bit," the former West Germany striker said.