Sadio Mane scored the quickest hat-trick in Premier League history, while Shane Long also netted a brace and Graziano Pelle completed the scoring.
The result leaves a huge dent in Tim Sherwood's managerial record since taking over at Aston Villa but restores some energy in Southampton's bid to finish the season on a high.
And Koeman - naturally - says he 'enjoyed' everything about the game. He also revealed the Aston Villa tactic Southampton 'punished' during the win.
Indeed, the Dutchman said Villa's high line and offside trap left plenty of space for Southampton, in not so many words suggesting it was completely the wrong approach.
The Saints boss told the BBC: "I enjoyed it very much, we played great football and with great spirit. Aston Villa played offside and with a high line and left us a lot of space and you have to punish that. We had great movement and passing."
Southampton's win takes them to the 60-point mark, while Aston Villa remain only four points above the relegation zone.
Hull City's defeat at Tottenham means Villa are safe regardless, although a 6-1 defeat is something Sherwood would no doubt hope his side would be looking to avoid regardless of their top-flight status!