The Premier League champions surrendered their 100% start to the defence of the title they won in such emphatic fashion barely two months ago.
Brazil international Alisson missed the game through a shoulder injury he picked up in training and his understudy Adrian conceded seven times as Liverpool sunk to an almost incomprehensible 7-2 defeat.
‘We don’t know exactly with this situation. It could have been worse with the injury, that’s for sure,’ said Klopp when asked how long the former Roma star would be out for.
‘We were slightly lucky but it’s not like he can play against Everton. I don’t want to put a timeframe on it… but four weeks is possible, six weeks more likely.
‘But I don’t know, we have to further assess this thing and that’s how it is.’
Liverpool have the next two weeks off and do not play again until October when they take on highflying Merseyside rivals Everton at Goodison Park.
Aside from the hapless Adrian, Jurgen Klopp could call upon 21-year-old Caoimhin Kelleher who impress in the domestic cup competitions last season, while Liverpool have also added teenager Marcelo Pitaluga to their goalkeeping ranks this summer.