Carvalho, was replaced by Firmino at half-time in the 0-0 draw with Everton after suffering a dead leg and now could be a doubt for the Champions League group-stage opener with Napoli on Wednesday night.
"It's not bad, I think," Klopp said. "It's extremely painful, a dead leg in the muscle above the knee. He couldn't bend the knee because the muscle has swollen up.
"When this muscle swells up, there is no space for anything else. "We will have to see how quickly that settles. You could see he tried, but you could see he couldn't run properly."
Klopp also revealed he is still needing to carefully manage the minutes of several Liverpool players.
The absence of several players through injury has been a major factor in Liverpool's stuttering start to the season - they have now dropped nine points in their opening six Premier League games - and Klopp admitted it is likely to be an issue for a few more weeks. Midfielders Jordan Henderson, Thiago Alcantara, and Naby Keita were among seven players unavailable for the match while new signing Arthur Melo was named among the substitutes but, according to Klopp, not deemed ready to play. Konstantinos Tsimikas started at left-back ahead of Andrew Robertson, while Trent Alexander-Arnold was taken off after an hour to manage his minutes. "Trent is playing all the time, Robbo (Robertson) is playing all the time and from time to time, like we have in the moment, we have alternatives there so that's why we have to use them," Klopp said. "That's why we have to use them to bring fresh energy on the pitch, pretty much. It's nothing to do with his performance, even when I know Trent can play better than today definitely but it's nothing to do with that. "We have to get through this period, how it is, because, yes, players are coming back but they have to be reintegrated. We cannot just bring them back to play 90 minutes or whatever, that's just not possible. "That's why we need to have a look where we can do the changes and give the game a new dynamic again." Darwin Nunez went straight back into the Liverpool side on his return from a three-match suspension, but had a frustrating afternoon as he was unable to convert any of the six chances that came his way. He was denied by a superb save from Jordan Pickford, who pushed his shot on to the crossbar late in the first half - one of three times Liverpool hit the frame of the goal - but was also guilty of missing the target with two headers from close range. "He had the start-stop integration, that's how it is," Klopp said of the summer signing. "We play all the time, that means we cannot train constantly, he was suspended in a week when we had two or three normal-ish sessions, the rest were individual when he had to do a bit more… "I know that he will score in these moments in the future, that is clear…No, it is not a concern or whatever, it is just the situation, it is all fine for the moment in that perspective."
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