The Saints got the better of City 4-2 at home in the Premier League on Sunday evening.
Sadio Mane was the star of the show for Southampton, as the 24-year-old Senegal international midfielder scored a brilliant hat-trick.
Kelechi Iheanacho scored both the goals for top-four-chasing City at St. Mary’s Stadium.
Koeman has taken to Twitter to revel in Southampton’s stunning victory over the Champions League semi-finalists.
Perfect afternoon in StMary's. Glorious victory with great goals and good teamwork. We continue our race for Europe. pic.twitter.com/qZT37jTV2O— Ronald Koeman (@RonaldKoeman) May 1, 2016
Over the course of the 90 minutes at St. Mary’s Stadium on Sunday afternoon, hosts Southampton had 40% of the possession, took 14 shots of which seven were on target, and earned eight corners.
The Saints are seventh in the Premier League table at the moment with 57 points from 36 matches.
Southampton will take on North London outfit Tottenham Hotspur away from home at White Hart Lane in the Premier League next weekend.