Koeman laments Southampton mistakes
The south-coast club's sparkling early-season form had been checked by defeats to Manchester City, Arsenal and Manchester United, though the trip to face Premier League strugglers at Turf Moor offered a chance to get back on track.
However, Southampton's profligacy in front of goal was capped off by Dusan Tadic failing to beat Tom Heaton from the penalty spot, before Ashley Barnes snatched the points for the hosts 17 minutes from time.
Despite enjoying the majority of good chances in the game, Southampton could not capitalise, leaving their manager frustrated.
He told BBC Sport: "Again, [it’s] the same story as last Monday against Manchester United. We had more chances, missed a penalty and one of our mistakes ended in 1-0.
"In my opinion, football is not that difficult but you can make it difficult.
"The difference between when we were winning games and are now losing them is a small detail like not punishing the opponent in a key moment like today. Also, doing more defensive mistakes.
"After a difficult start to the game, little by little we controlled the game. The story is to kill the game and we didn't. We paid for that.
"Everyone can make mistakes but too many goals in the last few games are from our own mistakes. We had enough chances to score but we didn't."