Liverpool took the lead in the 78th minute when substitute Christian Benteke met a precise delivery from captain James Milner with a towering header.But Mane bundled the ball in from close range after Gaston Ramirez headed James Ward-Prowse's free kick across the Liverpool goal four minutes from full time. The draw puts Liverpool ninth on 14 points, with Southampton a place above on the same total but better goal difference.
Liverpool's first-half display was full of the pressing from midfield which Klopp is known for, particularly in the early exchanges.
But Liverpool was toothless in attack. Southampton comfortably defended its own penalty area and reduced the hosts to shots from long range, while beginning to pose problems in attack as the half progressed.
Klopp responded by replacing striker Divock Origi, who started the game as Daniel Sturridge missed his third straight match due to a knee problem, with Benteke.
Liverpool and Napoli left with work to do after Anfield draw