With Alisson facing two months out with a calf injury, the Spaniard is now Liverpool's outright No1.
Speaking to the club's official website, Klopp said: "I'm not worried at all about how he will do it in the long term, but in the short term the problem is just that he came here with no club when we signed him.
"We don't have to talk too much about it, that's what the experience is for.
"He looked very good and very sharp from the first session he had with us but of course now we need to be careful [and] pack him in cotton wool pretty much.
"We cannot now do the hardest training with him every day and stuff like this, we have to make him match fit every day, that's how it is. So that's what we try and then he will be fine.
"He's a really, really good goalie and a really good person and since he was in he looked really well, and that's it."