The Dutchman oversaw his first game since arriving at the Premier League club in June as Southampton beat EHC Hoensbroek 4-0 in Netherlands on Tuesday.
Koeman was delighted with the way his squad approached the match against the Dutch amateur side as they scored twice in either half to get his reign off to a winning start.
"You can see the group is growing up in a physical way and playing in the way we like to," he told the club's official website.
"It's always a tough week when you have a lot of training sessions and play two friendly matches, but we are very happy with how the players are acting.
"They are doing a professional job, and I am very happy about that.
"Now we are looking forward to Thursday, when we play our second game (against KSK Hasselt). We will finish this week well – and if we get back to Southampton without injuries, then that's even better."
Following the KSK Hasselt clash, Southampton return to England for friendlies against Swindon Town, Bournemouth and Brighton and Hove Albion.
