The £4.7million summer signing from Mainz has flown home from the club's tour of America after breaking a bone in his right hand.
Karius is facing surgery and will be sidelined for up to 10 weeks.
Klopp insists he hadn't yet decided who would be No 1 come the trip to Arsenal on August 14 but Mignolet is now certain to start ahead of veteran Alex Manninger.
Asked about the blow of losing Karius, Klopp said: “You never want an injured player and there’s never a good time with the timing of injuries.
“It’s not cool for him, not cool for us but it won’t change and we have to take it.
“We have another three goalkeepers. Everyone knows about the quality of Simon Mignolet. He’s made a really good impression in the first few days back in training and we also have a very experienced one in Alex Manninger and a very young one in Shamal George.
“A broken bone in the hand for a goalkeeper isn’t great. It’s not the worst but it could have been even worse. Six, eight, 10 weeks out, whatever, is not the longest period but it’s not too good either.
“It's not that I'd decided who was No 1. It was just about collecting information about the two players. “It was a battle between him and Simon and now that battle is decided for the next few weeks 100%.
“I’m of course really happy we have Simon and hopefully he will stay in the race and not get injured. We will need to give the other two match time now too.”