The Saints managed to pick up a point against Remi Garde’s struggling side when Oriol Romeu netted a late equaliser.
However, Koeman was frustrated by his team’s lack of ruthlessness in front of goal and insists his players should be showing more quality in the final third.
"Congratulations to the players, their belief and spirit," Koeman is quoted as saying. "We kept that until the last seconds. [But] if you get four big chances and not one on target, I don't understand.
"At least in the box, close to the box, the shot has to be on target. Maybe it's a lack of confidence but they are quality players and they have to bring more."
The likes of Sadio Mane, Graziano Pelle and Dusan Tadic all had opportunities during the stalemate, which Southampton largely dominated.
The Saints had 23 shots in total against Villa but they only hit the target on five occasions and that ultimately cost them their chance of claiming all three points.
Southampton are now winless in their last four matches and will be keen to get back on track quickly.
The Saints have made an encouraging start to the season but they will be eager to ensure they don’t slip any further down the standings.
Koeman’s men are now in 12th place in the Premier League table but are only two points away from a European qualification spot.