Mane joined from Liverpool for £34m while De Ligt signed for £68m from Juventus.
The pair come with big reputations, with Mane winning every available major club honour with Liverpool and is also the reigning Africa Footballer of the year while De Ligt is one of the most highly rated young centre backs around.
Bayern have also added Ajax pair Noussair Mazraoui and Ryan Gravenberch to their ranks but suffered a major setback when Robert Lewandowski pushed through a move to Barcelona.
Writing in his column for the Sportbuzzer, Rummenigge opined: "Why has Hasan Salihamidzic Co. been praised for recently for their summer transfers? Honestly, I can't join in this chorus of jubilation."
"With all due respect for Sadio Mane and Matthijs de Ligt - both of them are not world-class players for me. Of course, Mane will do the Bundesliga good and score his goals, but at the age of 30, I don't see him at the absolute top level."
"Had it been otherwise, Jurgen Klopp would have certainly fought harder to keep the striker at Liverpool."
"I'm even more sceptical about De Ligt. Sure, he's only 22 years old. But the last three seasons at Juventus were lost time for him," Rummenigge added.
"He should have been able to develop further after his furious start to his career at Ajax. I think it is very daring to declare him Bayern's chief of defence. You could have kept Niklas Süle."
Mane started and scored as Bayern Munich defeated RB Leipzig 5-3 in the German Super Cup on Saturday while De Ligt was a second half substitute.
