The Reds got back to winning ways thanks to a brace from Mohamed Salah and a wonderful strike from Diogo Jota, taking them up to second in the Premier League table heading into the international break.
"In this part of the season, a lot of teams struggle a bit with injuries. It's the same for us in the moment, so that's how it is and we have to deal with it, and we do that."
While Klopp didn't shed a lot of light on Konate's fitness concerns, journalist Hawkins took to social media to offer an update on the French centre-back's injury.
Writing on X, Hawkins said of Konate: "Victim of a small muscle injury to the left hamstring with Liverpool in the Europa League on Thursday in Toulouse during the warm-up, Ibrahima Konaté was unable to play this weekend with Liverpool.
"His injury requires approximately two weeks of treatment."
If Hawkins' diagnosis is correct, Konate won't be able to travel with France during the international break. The 24-year-old was included in Didier Deschamps' squad for matches with Gibraltar and Greece, but will no longer be able to team up with Les Bleus.
However, if Konate is missing for just two weeks, there is a chance that he returns in time for Liverpool's trip to Manchester City after the international break.
The Reds travel to the champions in Saturday's early kick-off on 25 November and Klopp will want Konate back to help deal with Man City's immense attacking threat.
The Liverpool defender has been regularly sidelined with injury since arriving at Anfield, however, he normally recovers fairly quickly to take his place back in Klopp's side.