Despite his side being unbeaten in their last five and taking ten points from a possible 12, the Dutchman is not completely satisfied.
Koeman was disappointed with how Saints fared in the final third during their recent trips to Manchester United and Arsenal, saying that he expects more when they host West Ham United on Saturday evening.
“We create chances but we need to be more clinical in our final pass,” he told the media on Friday afternoon.
“Our final pass was not good against Man United and was not good at Arsenal, but [we won] four points.
“Our last pass was not the best what we can bring, and that we need for tomorrow.”
Koeman gave his backing to forward Sadio Mané, who has not scored for 14 league games – but says competition for attacking places is building.
“What I mention as that he (Mané) is working hard, but he needs to improve in that final part to attack,” said the manager.
“That goes for Sadio and for all the strikers. It’s about the productivity of the strikers.
“[Steven] Davis is coming back, Charlie [Austin] is coming back, [Graziano] Pellé is back and, maybe in two or three weeks, Jay Rodriguez will come back. That’s a lot of competition for them.
“Finally, as the manager, you choose the best options to start and it’s up to the players.”