Liverpool suffered their second Premier League defeat of the season in Southampton (1-0), a third consecutive winless match for Klopp's side who now share top spot with Manchester United.
Twenty-four hours after Chelsea's collapse against Manchester City (1-3), Liverpool are the second major defeat of this 17th matchday that completely shuffled the cards.
The Reds retain their top spot for goal difference, but risk finding themselves behind Manchester United, who will play at Burnley in the January 12 postponement.
Southampton's winning goal was scored by Danny Ings after not even a minute of play.