The Roten chief says last weekend's European triumph was the biggest in the club's history but thinks a repeat of the period of domination in the 1970s is no longer possible.
The former striker was part of the side that lifted the famous trophy for the third successive time in 1976, but the current Bayern CEO believes last Saturday's win over Borussia Dortmund surpasses both that achievement and the 2001 final victory over Valencia.
"What I have experienced now is above what we had then and above our triumph in 2001," Rummenigge told Bild. "However, I believe such an era [of dominance] is no longer feasible because the European top two or three percent today decide on the destiny of the trophy."
The Bundesliga winners are on the brink of German football history as they chase an unprecedented treble in the final of the DFB Pokal on Saturday, and the former Germany international says the team can become 'immortal' with a triumph over Stuttgart.
"It would be nice if we win the treble," Rummenigge said. "The question is whether the team can do it after the triumph in the Champions League. Once again, we need to keep this concentration and this greed as high as it has been in the past three or four months.
"The final last Saturday really was second to none. Nevertheless, one has the impression that our players really want this treble. I know that they can become truly immortal now."