However, Mane, who was sent off in the closing seconds with a second yellow card, bundled home a scrappy leveller with three minutes remaining to win a point for the Saints.
Here, Sports Mole reviews the action from Merseyside on an evening when Klopp's winless streak extended to three games.
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On target: 2
On target: 3
Was the result fair?
Southampton deserved a point to bring with them on their long trip back to the South Coast. They were comfortably the better side in a first half which saw them miss a couple of excellent chances. They were out-played and out-fought for large spells of the second half, but their efforts during the opening 45 minutes certainly merited a point.
Not for the first time under Klopp, Liverpool looked excellent defensively but there was a glaring lack of cutting edge at the other end of the field; one that will not be solved by a fully-fit Benteke or Daniel Sturridge. It was their creative talents which once again looked ineffective.
Philippe Coutinho, in particular, still does not look the same player he was under Brendan Rodgers. He was woeful here again for the most part, following on from anonymous displays against Spurs and Rubin Kazan. Ahead of him, Origi, another who has started all three games in the Klopp era, looked poor.
Only when Origi was replaced by Benteke did Liverpool start to look dangerous. The big Belgian lifted his teammates, but it was not until the 77th minute when he got a clean sight at goal. He made no mistake, planting a quite brilliant header past the helpless Maarten Stekelenburg.
Still, it was not enough when it should have been. Defensively, Liverpool looked solid for 86 minutes, but questions will be asked over why Mane, Southampton's most dangerous player, was allowed to wander into the box unmarked and bundle home the equaliser to spoil the party. Klopp smiled on the outside. Inside, he will be furious and rightly so. He reiterated during the week that he was no miracle worker, and this result is certainly proof of that.
With victories at Arsenal, Manchester United and Chelsea over the past 13 months, Southampton, under Ronald Koeman, certainly have the pedigree for an upset, and the prospect of another looked good during the first half. They were better than Liverpool for the majority of it, with Virgil van Dijk missing a gilt-edged chance to yield something tangible for their dominance.
They defended well, too, with Jose Fonte and Van Dijk consigning Origi to just 13 touches in 45 minutes, while the fit-again Jordy Clasie lived up to his surname. The Dutchman was excellent as he stifled the creative talents of Adam Lallana. Koeman would not have found much fault with his troops' first-half display, but it was a different story after the break. Suddenly, Liverpool were much the better side, with Benteke proving much more problematic than Origi had done.
Even then, Fonte had dealt with the ex-Aston Villa man well, but the Portuguese let Benteke get the run on him for the goal. The Saints never looked dead and buried, though, and James Ward-Prowse - who replaced the anonymous Dusan Tadic - swung in an excellent delivery for the free kick which led to their timely, and deserved, equaliser.
Sports Mole's man of the match
Christian Benteke: Despite only coming on at half time, Benteke was easily the stand-out candidate for man of the match in a game which, in truth, lacked a lot of individual quality at times. His arrival restored Liverpool's impetus following a relatively flat opening 45 minutes in which Origi had little impact, before sending a wonderful header past Stekelenburg.
James Milner conceded a needless free kick from which Southampton's equaliser stemmed from, but Van Dijk should have opened the scoring when he missed a free header from point-blank range in the first half.
Andre Marriner had very little to do for the best part of 86 minutes, when he produced his first yellow card of the evening to correctly book Milner. He went on to show the yellow two more times, and then a red when Mane was sent off for two silly fouls in stoppage time.
Liverpool: The Reds are back at Anfield on Wednesday for a fourth-round Capital One Cup clash with Bournemouth.
Southampton: Also returning on Wednesday for League Cup duty, Koeman's men host struggling Aston Villa.