Alisson picked up his issue in the latter stages of the clash with the Premier League champions, while Jota was withdrawn early in the second period of what proved to be a 1-1 draw.
Klopp has revealed that Alisson will be missing for at least two weeks with his problem, while the Liverpool head coach said that Jota would be out for "a little bit longer".
"Both are out. Ali is a bit lesser, so we have to see. Not day by day - he cannot play tomorrow [Thursday] or Sunday. Probably not the week after should be kind of OK," Klopp told reporters ahead of Thursday's Europa League clash with LASK Linz.
"Alisson is not as bad [as we thought] but still bad enough. Diogo will take a little bit longer, don't know exactly. Have to see."
Alisson is set to be absent for up to five matches, but he could return for the Premier League clash with Manchester United on December 17.
Jota, though, is seemingly now a doubt for the festive period, with the 26-year-old's issue more serious than the one his teammate suffered at the Etihad Stadium.
The forward has netted eight times in 17 appearances during the 2023-24 campaign, including four goals in 12 outings in the Premier League.
Liverpool are in a strong position at the top of Group E, collecting nine points from their four matches, which has left them two points ahead of second-placed Toulouse and five ahead of third-placed Union SG.
A win or a draw on Thursday would therefore see the Merseyside outfit secure their spot in the knockout round of the Europa League with a game to spare.
Caoimhin Kelleher will now be given a run between the sticks in Alisson's absence, and Klopp has insisted that he has no fears over selecting the 25-year-old.
"That's why we knew we wanted to have Caoimhin here - for these moments. Nobody, Caoimhin [included], wanted Ali to get injured but if these kind of things happen then you need the strongest possible option and that's Caoimhin for us.
"That's the only positive about that, to be honest, we can put in Caoimhin and that's fine. Now he gets the opportunity, which he deserves anyway, he would have played tomorrow night anyway, that's clear.
"But now he will have a few more games and hopefully he can show his full potential."
As well as Alisson and Jota, Liverpool are currently without the services of Thiago Alcantara, Andrew Robertson and Stefan Bajcetic due to injury problems.