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Despite trailing initially, the Reds managed to secure a win, pushing them 16 points ahead at the top of the Premier League table with two games in hand before Arsenal's Sunday match against Manchester United.
Will Smallbone shocked Anfield by scoring just before half-time, putting the Saints in the lead.
The former Premier League referee has argued that Smallbone's goal should have been disallowed for offside by VAR.
The Southampton midfielder capitalised on a mix-up between Virgil van Dijk and Alisson to gain control of the ball near the six-yard box.
Replays suggest that Mateus Fernandes had slipped past the Liverpool goalkeeper to snatch the ball.
A screen shot of the incident between Alisson, Matheus Fernandes and Will Smallbone(Image: Sky Sports)
The legitimacy of the goal has come under scrutiny, with Smallbone potentially offside in the build-up to Southampton's strike against Liverpool.
Despite Fernandes' forward pass, which seemed to place Smallbone ahead of the Reds' last defender and keeper, Alisson, the Video Assistant referee did not spot an infraction.
So, Matt Donohue allowed the on-field referee, Lewis Smith, to uphold the goal.
The Southampton player has gone to challenge the keeper.
Virgil van Dijk, Will Smallbone and Alisson during the controversial incident(Image: AP)
"It's touched his foot and gone forward and Smallbone's left foot seems to be in front of the defender.
Unless there was another defender outside that we can't pick up on the TV, but he looks offside in my opinion."
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After losing 3-1 to Liverpool, Southampton find themselves marooned at the bottom of the Premier League with just nine points, trailing the 17th-placed Wolves by 14 points.
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