The Saints suffered a 2-0 loss to Bournemouth away from home at the Vitality Stadium in the Premier League.
Bournemouth took the lead just past the half-hour mark when Fraser Forster parried Matt Ritchie's free kick and Steve Cook volleyed in.
Benik Afobe added the second on 79 minutes when he headed in at the near post from another Ritchie free kick.
Koeman has taken to Twitter to give his reaction to the defeat, claiming that Bournemouth were sharper that the Saints.
They were more sharp than us from the start!— Ronald Koeman (@RonaldKoeman) March 1, 2016
Over the course of the 90 minutes at the Vitality Stadium, hosts Bournemouth had 45% of the possession, took nine shots of which four were on target, and earned 10 corners.
Visitors Southampton had 55% of the possession, took six shots of which only one was on target, and earned two corners.
Southampton are now seventh in the Premier League table with 40 points from 28 matches.