The influential Brazil international has become a major component in the team's rise to the top of the Premier League, but he was forced off with an ankle injury in the 1-1 Champions League draw with Napoli.
He left Anfield with his left foot in a protective boot and Klopp will hope he is not ruled out for any length of time with a packed December fixture schedule coming up.
"In this moment, the game is over, my problem is Fabinho is injured and Brighton [is on Saturday]," he said after Dejan Lovren's header cancelled out Dries Merten's contentious opener.
"I don't know [how he is]. He has pain, so that's not good. He couldn't continue and he is a really hard one.
"I don't want to say what I expect, because I hope that it is not that serious, but we will know more, maybe today, maybe the day after. We will see."
Failing to beat Napoli means Liverpool must now go to Red Bull Salzburg in their final Group E match and get a point to ensure progress to the knockout stage.
It would have made things much easier for Klopp had that game been a dead rubber but as qualification is still not guaranteed he cannot afford to rest his star players.
It is a slightly easier ask than last December, however, when their fate went down to virtually the last kick of their final game - at home to Napoli - when Alisson Becker's added-time save secured a 1-0 win and passage to the last 16 from where they went on to win the competition.
"I'm four years in, tell me when it was easy," Klopp said.
"Last year we had to win at home 1-0 against Napoli, I cannot remember a bigger pressure game than that. So, really difficult, and we did it.
"I know how human beings are; people wished we could finish the group tonight and make kind of a holiday game in Salzburg.
"That's the situation: if we have ambitions in the Champions League, we have to show that in Salzburg. Until then, we have to show our ambitions in the Premier League."