Woltemade struck as Newcastle defeated Nottingham Forest 2-0 on Sunday.
Earlier in the week. Bayern Munich board member Rummenigge branded Newcastle "idiots" for paying €90m to Stuttgart for Woltemade.
"I really like him and I actually saw that quote a few days ago and it angered me and I am not a Newcastle United supporter," Carragher told Sky Sports.
"I think it is a joke really coming from someone who is part of a football club, in terms of Bayern Munich, a really respected football club.
"He shouldn't be speaking about, especially, another German player like that so disrespectfully. That would have been all over the news in Germany and his family and friends are there.
"That is our job, we are pundits, not somebody who is associated with such a fantastic club. That is really disrespectful and when I saw that I thought: 'Do you know what? I really hope that lad shoves those words down his mouth'.
"And at the start of his Premier League career it looks like he is going to do."