Wirtz completed his move from Bayer Leverkusen to Liverpool on Friday.
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He has joined the Reds for a fee rising to £125m - a British record.
"Fundamentally, I think it's a shame. We've always had the philosophy that the best German players should play for FC Bayern," Rummenigge, who remains an advisor to Bayern, told De Welt.
"We gave it our all; in this case, no one made a mistake. It's Florian's decision – and we have to accept it."