Southampton have scored 11 times in their last three matches.
The Saints started the season slowly, with their goalscoring issues something of a concern, but they have started to find their groove in recent weeks.
Southampton have scored 11 times in their last three matches, and Koeman has hailed the ruthless nature of his side's finishing.
"Before we needed too many chances to score goals, or to kill the game but that's changing," the Dutch boss said.
Southampton have had to develop a cutting edge to their play, as their profligacy was letting them down at the start of the campaign.
The Saints were creating a number of chances, but being wasteful, and they have had to work hard on their finishing to ensure that they have pushed up the table.
The likes of Shane Long, Graziano Pelle, Sadio Mane and Jay Rodriguez have all been among the goals of late, with Koeman's side starting to click into gear.
The Saints now sit in 10th place in the Premier League table, with a fixture against out-of-sorts Chelsea next on their schedule.