Lovren, 28, was at fault for two of Tottenham's four goals last Sunday as Mauricio Pochettino's side earned a comfortable 4-1 victory at the Wembley Stadium thanks to goals from Son Heung-Min, Dele Alli and a brace from Harry Kane.
The Croatia international was even withdrawn before the half-time whistle by Klopp and it now remains to be seen if the German manager will hand the former Southampton defender a second chance against Huddersfield.
However, former Liverpool player Thompson told the Liverpool Echo that he believes Lovren must be taken out of the firing line against David Wagner's side with scrutiny from fans and the media still likely to be ringing in his ears.
"I would have to take him out of the firing line. After what he went through at Wembley, I think it's too raw at the moment to play him again so soon," Thompson said.
"Jurgen will have to make changes. If he doesn't have faith in Ragnar Klavan then he has to go with Joe Gomez in there alongside Joel Matip. We have a run of winnable games coming up and we have to make sure we're more solid at the back."
Cameroon international Matip partnered Lovren in the middle of Klopp's back four against Spurs and he is likely to do so this Saturday, with either Lovren, Gomez or Klavan set to partner him.
Klopp must be wary of Huddersfield's threat come Saturday, with the Terriers squad likely to be in buoyant mood following last Saturday's stunning 2-1 victory over Manchester United.