Klopp's side battered the Red Devils at Old Trafford as Mohamed Salah scored a hat-trick in a 5-0 victory.
Solskjaer is now under pressure to keep his job, and Klopp admits he feels sympathy for the Norwegian.
"Of course [I have sympathy]," Klopp told reporters after the match.
"The last thing I'd want to be is in his shoes in this moment.
"In the moments when you lose a derby you don't want to go and answer questions, so it's for sure not nice for him."
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