Shane Long scored the only goal of the game as Saints extended their run of clean sheets to six games thanks to another shut-out against the Swans.
Koeman, who thanks to the win picked up his 100th point as Saints boss in the Premier League, was again happy with the all-round team display.
“I’m very pleased because it was a difficult game. In the first half we had good defending but our ball possession was not what we like,” Koeman told youtube.com/southamptonfc
“The second half was much better in that way and still good defending. We had the best chances in the game – already in the first half a fantastic cross of Steven Davis and a free header of Shane.
“The second free header was a goal and a fantastic cross of Prowsey (James Ward-Prowse). Shane scored the 1-0 and after that it looks very comfortable.
“We were strong defensively again for the three points.
“Even in difficult periods in the game we are looking sure about ourselves. We don’t make stupid mistakes at the moment and we keep believing we can score.
“That’s an important factor what you need.”
Koeman was quick to praise the whole team for adding another clean sheet to their run. “At the moment it’s really good defending, but you see how the boys are working in front,” he added.
“In the midfield they press and the five at the back defensively are very strong. The goalkeeper looks very confident.
“It’s not easy to score against Southampton.”