Liverpool goalkeeper Karius fumbled Christian Pulisic's shot as Jacob Bruun Larsen scored Dortmund's third goal in stoppage time after an earlier unpunished lapse when he sliced a clearance straight to Maximillian Philipp on Sunday.
Liverpool manager Jurgen Klopp has backed the former Mainz stopper to learn from his mistakes, though the Reds have since signed Alisson in a world-record deal for a keeper.
Karius used Instagram to respond to his detractors amid the ongoing scrutiny.
"To those who take joy in seeing other people fail or suffer, I feel for you," the 25-year-old said in a messaged posed on Sunday.
"Whatever it is that is happening in your life to hold this much anger and hate, I pray that it passes and good things come to you."
Klopp is not the only one who is tired of Karius' critics, as former Madrid and Spain captain Iker Casillas also came to the defence of his fellow stopper.
"This attack on Loris Karius, will it ever end? I’m talking about him like so many other goalkeepers," the 2010 World Cup winner said via Twitter.
Este ataque a @LorisKarius va a terminar alguna vez? Hablo de él como tantos otros guardametas. Hay muchos más problemas serios en el mundo joder! Dejar al chaval en paz! También es persona. Como lo somos todos!— Iker Casillas (@IkerCasillas) July 22, 2018
"There are many more serious problems in the world… f***!
"Leave the kid alone. He is also a person. As we all are!"