The Saints came from two goals down to get the better of Liverpool 3-2 at home in the Premier League on Sunday afternoon.
Philippe Coutinho and Daniel Sturridge put the Reds in the lead after just 22 minutes, but second-half goals from Sadio Mane (two) and Graziano Pelle saw Southampton pick up all three points from the encounter at St. Mary’s Stadium.
Koeman has taken to Twitter to revel in his side’s superb victory over Jurgen Klopp’s Liverpool.
The win against Liverpool means that Southampton are now seventh in the Premier League table.
The Saints are just four points behind fourth-placed Manchester City, who have a game in hand.
A top-four finish is not entirely out of reach of Southampton, but they will face stiff competition from the Citizens, West Ham United, Manchester United and Liverpool.