The Brazilian pair were both taken off in the win over Sunderland.
The Reds won 2-0 against the Premier League's bottom side on Saturday, but the victory was marred by a horrible-looking injury to Coutinho, who was stretchered off after little more than half an hour.
Then, late in the game, Firmino also had to be replaced after picking up a knock which prevented him from carrying on.
The two blows will have Liverpool fans seriously worried. The Brazilian pair are key to the club's title hopes, racking up 10 goals and eight assists between them in the Premier League so far this term.
Speaking immediately after the game, Klopp said that he cannot comment on how bad Coutinho's injury could be until the player's ankle is scanned.
The German boss said, via BBC Sport: "It [Philippe Coutinho's injury] is an ankle injury but we can't say anymore until we see a scan.
He then added, as quoted by the Liverpool Twitter account: "We have to wait for the scan. When I saw him at half-time he said there was no pain."
However, he did move to relieve fear over Firmino's problem by suggesting that the forward's calf knock does not seem like it will be a serious issue.
He added: "Firmino got a knock on the calf as well. That should not be that serious."
Liverpool will be desperate to have that confirmed and see Firmino return as soon as possible, particularly as it looked for all the world as though Coutinho is likely to be set for a considerable injury lay-off.