The Reds maintained their perfect record with a third successive win thanks to goals from Danny Ings and Ben Woodburn but the afternoon was blighted when Matip limped off in the final minutes.
The defender was one of just three players to last the full 90 minutes, with slight problems for Marko Grujic, Alberto Moreno and Brad Smith having left Klopp with just eight substitutes.
But though Liverpool were forced to see out the dying stages with 10 men after Matip walked down the players' tunnel in discussions with the club's medical staff, Klopp is confident his problem isn't a serious one.
With Mamadou Sakho and Joe Gomez already set to miss the start of the coming season with Achilles-related issues, and back-up Tiago Ilori absent due to his involvement at the Olympic Games, the German will be aware that any further injuries leave him lacking options at the back.
Reds defender will be back by Tuesday, suggests Klopp
"I hope it's only a minor problem," the Reds boss said after full-time, revealing that the Cameroon international has suffered from the same problem "one or two times already."
Klopp told journalists that Matip's knock was "the [same] foot he had problems with in the past" and admitted the defender had felt "a little bit of pain when pre-season started" due to "the intensity" and the strain on his pre-existing problem.
The Bochum-born 24-year-old recently had minor surgery to take out pins that were put in his ankle a few years ago, with Klopp dismissing Matip's pain and insisting that he's "used to it."
"Joel gets better and better and better, you can see it," continued the manager, adding that "it's not too serious, hopefully."
He added that he hopes Matip's injury "is like this" because "everyone can see he's in a real good way" and insisted: "I think tomorrow, he'll rest and then he can go again [in training on Tuesday]."
Klopp revealed that he and his backroom staff were forced to "make the decision" between whether Matip or Dejan Lovren would play the entire game, given his limited numbers.
He admitted that 90 minutes was "a little bit too much" for Matip on the day, but insisted that he is still "in a good way" and should re-join the ranks later in the week.