The reds have suffered several setbacks in recent weeks with the latest coming at the Saint Mary’s Stadium.
Danny Ings’ brilliant finish in the second minute of the first half settled the contest and put the Saints to a fine start of the game against his former club.
The lost to the Saints means the reds have taken only two points from a possible nine but remain top of the table on goal difference.
Both Manchester United and Manchester City will leapfrog the reigning champions if they win their games in hand.
Southampton’s win pushes them to sixth on the league table and brought an emotional response from manager Ralph Hasenhuttl, after taking points against a side side led by Klopp for the first time.
The hosts were good value for their victory, forcing the pace early on against an unfamiliar Reds backline containing Jordan Henderson, and then defending resolutely as the visitors poured forward after the break.
Liverpool’s next league fixture will be at home to Manchester United who are in some great form and would like to take advantage of Jurgen Klopp’s side.
