Reds centre-back Ibrahima Konate suffered a knee injury in the friendly against Strasbourg on Sunday which Klopp said will see the defender out "for a while".
Konate has joined a list of sidelined Liverpool players that already includes Kostas Tsimikas, Alex Oxlade-Chamberlain, Diogo Jota Curtis Jones and reserve goalkeeper Caoimhin Kelleher, with Naby Keita set to resume training on Friday after nearly a week out with illness.
None of the absentees are understood to be suffering with long-term injuries, however.
Liverpool have made three major pre-season signings in Darwin Nunez, a £63 million ($77 million) from Benfica, with Fulham teenager Fabio Carvalho (£5 million) and Aberdeen defender Calvin Ramsey (£6.5 million) also arriving at Anfield.
"We have too many injuries, that's true," said Klopp speaking Friday on the eve of Liverpool's Premier League opener away to Fulham.
"But in the moment nothing has changed (in terms of new signings). A lot of unlucky situations. Started with Caoimh and Diogo, pretty much one was injured and one had a re-injury.
"In a few weeks' time they will be back, but they've missed pre-season and that's not cool.
"Ibou in a challenge in the game against Strasbourg, what happened there we have to see how long it will take but he's out for a while."
But the German boss, who saw his side just denied a historic quadruple last season after Manchester City pipped them to the Premier League and Real Madrid beat Liverpool 1-0 in the Champions League final, was cautious about re-entering the transfer market.
"We cannot solve a problem we have for four weeks with a transfer for a full year," he said. "That makes at the moment no sense to us.
"The transfer window is still open and we will see but the plans are not to go in that direction."
One positive piece of news for Liverpool on the fitness front is that goalkeeper Alisson Becker will be available to face Fulham after missing most of pre-season with an abdominal injury sustained on a tour of the Far East.
Nunez could also feature against the Cottagers after scoring as a second-half substitute in last weekend's FA Community Shield win over Manchester City.
"Darwin is ready, but does that mean he has to start? I don't know," added Klopp.
"We have different options and that is what we will use and Darwin needs time to get used to a lot of things."
Klopp added: "He is completely settled. He said himself he was very nervous in the beginning and I sympathise with that a lot, it's normal.
"But he settled pretty quickly because of all the players, not only the Spanish speakers, and that was very helpful and he feels at home after a short period.
"He had a real impact in the first final we could have played but the work will not stop and he is in the best possible place."
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