For keepers I don't think what happens in training plays a big part. Ultimately a keeper can be perfect in training all week and 89 minutes during the game but if they make 1 mistake that's all that counts.
Klopp spoke about the situation during his press-conference, saying there is no number 1 right now and brought up a number of possible scenarios - one being that he might play Karius until the next international break and then both keepers have had a run each, and he'd make his decision from there. The reality is that he signed Karius to be number 1 and he's brought him in as soon as he could. The way it's played out has made it a bigger call than it might have been and it's put more pressure on Karius to perform.