The Brazilian stayed down after the follow through of a Didier Ndong clearance caught his right foot and he had to be stretchered off in serious discomfort.
Coutinho's replacement Divock Origi ended 75 minutes of frustrations when he broke the deadlock, finding the far bottom corner at the Kop end after the Reds had gone agonisingly close on a number of occasions.
James Milner wrapped up the victory late on with an assured penalty after Sadio Mane had been brought down by Ndong and asked whether he could issue an update on Coutinho post-match, Klopp said: "Unfortunately not. We have to wait for scans."
The manager confirmed that what the club know "in this moment" is that Coutinho's issue is "something with the ankle" and added: "That's it. We all have to wait."
Coutinho wasn't in pain by half-time, says Klopp
Klopp also added that while the 24-year-old's injury "in the first moment" was "obviously very painful", by the time they saw each again at half-time Coutinho informed him that his problem was "much better" and that he had "no pain."
"But it's how I said. We have to wait. I have no idea what it is," continued the German, who said that he cannot imagine "how long" Coutinho's problem could see him out for.
Klopp did however insist that he is "quite optimistic" and hoped that the Reds' No.10 could even be back in training by Sunday.
Any serious problem would be a damaging blow to Klopp's charges, with the in-form Coutinho having been the orchestrator of many of their wins this season.
On Liverpool's other knocks, Klopp was evidently frustrated with the decision of referee Anthony Taylor not to award a foul on Roberto Firmino late into the second-half.
He continued: "Yes, I thought it was a foul. Firmino's [injury is] much better than Phil, but he has pain in the calf."
Daniel Sturridge was missing from the teamsheet, having been ruled out beforehand with a minor calf strain, and the manager also said that his absence was due to a "tight calf" which meant the striker hadn't trained for two days.
Klopp insisted: "I have no idea when he will be back. He can't train tomorrow because of this injury."