The Reds came closest to breaking the deadlock when James Milner saw a second-half penalty saved at the Kop end but couldn't earn the rewards for their dominance as the game ended goalless.
For the fourth match in a row, Jürgen Klopp named the same starting XI, with Philippe Coutinho having recovered sufficiently from a dead leg sustained against Watford to keep his place.
And fittingly, given the sunny conditions, the Reds made a bright start.
Roberto Firmino's relentless pressing presented the first good opportunity, but the Brazilian's effort after pinching the ball was blocked before Southampton managed to scramble the ball away.
Aside from that early chance, the visitors gave little away as they stuck doggedly to their defensive task, largely restricting Liverpool to efforts from distance.
Two such attempts - weaks shots from Firmino and Emre Can - proved to be the closest the hosts came in first 45 minutes as they headed in for the break with plenty still to do.
The second period started in the much the same vein, with Southampton content to sit in and guard the Kop-end goal while Liverpool probed a solid backline.
But the Reds were handed a chance to break that resistance when Jack Stephens inexplicably elbowed a high ball into the box away and referee Bobby Madley pointed to the spot.
However, Fraser Forster granted the visitors a reprieve with an excellent save from a Milner spot-kick attempt that looked destined for the bottom corner.
That disappointment prompted Klopp into action, with the boss introducing both Adam Lallana and Daniel Sturridge in an attempt to spark his attack into life.
With 15 minutes remaining, the pair linked up well to create space for Coutinho, whose left-footed attempt was easily collected by Forster.
And it was a similar story moments later as Sturridge poked a shot goalward from his fellow Englishman's clever pass, but again he was denied by the 'keeper.
Liverpool's subsequent attempts to break the deadlock were repelled by some desperate Southampton defending - and a fine Forster save from Marko Grujic's header - as they ensured their a fourth clean sheet in as many games against Klopp's team this season.