Klopp made nine changes to his starting eleven, with James Milner and Lovren being the only two to retain their place from Thursday night's defeat at Man City.
And Lovren was forced off within the opening five minutes after signalling an injury to the bench, with youngster Ki-Jana Hoever replacing him in the back-line.
Speaking after the game, Klopp confirmed that Lovren suffered a hamstring injury, whilst praising Hoever's performance.
Klopp told his post-match press conference: “[It is his] hamstring, is what I heard - without any signs before. I asked everybody, no signs, nothing, just out of the blue, so that's the decision you have to make.
“I am not sure what you all would have said if immediately from the beginning if our centre-half situation was Fabinho and Ki-Jana; then probably a few very smart people would tell me that I don't respect the competition or whatever.
“So, we tried to do all the things [we could]. Of course, on the other hand it doesn't make sense to bring in a 16-year-old boy from the start.
“You don't bring him, you wait until he is completely ready, but he did well. He came on and did well. That's how it sometimes starts - when you are really needed then it is only about if you are good enough and not how old you are. He did well, so that was all OK. That's it.”
The boss added that he hopes either Joe Gomez or Joel Matip can return to full training ahead of this weekend's trip to Brighton.
The duo have been out of action since December, leaving Klopp with just Lovren and Virgil van Dijk at the heart of defence.
It remains to be seen whether Gomez or Matip can return in time, with Lovren facing a spell on the sidelines.
One option for the Liverpool manager is to draft in Brazilian midfielder Fabinho in to the back line, as he did against Nuno Espirito Santo's side.
Klopp previously spoke of how he will "not sign a defender" in the January transfer window, but Lovren's injury may prompt him to re-think his transfer plans.