A Dusan Tadic penalty and Nathaniel Clyne's long-range strike saw the Saints come from behind to win 2-1 at the Emirates Stadium and continue their promising start to the season under their new manager.
"I'm very proud, because winning away against Arsenal, that means a lot," Koeman told reporters. "Everybody spoke about the changes of the Arsenal team. I think they made some changes but they took it very seriously.
"I think the game was on a very high level, with high tempo, and I enjoyed it. I enjoyed tonight, not only for the result finally, but the way we played.
"We tried to press and tried to play attractive, offensive, and that's not easy, because they have a great team, great players."
Southampton are currently second in the Premier League table, having collected 10 points from five games.