The Saints put eight goals past their hapless opponents as they moved up to third in the Premier League table.
Koeman told reporters: "I'm still in a little bit in shock. Not about the second half, I think we played very good and scored some great goals, but about the first 20 minutes because I wasn't very happy about our performance at the beginning.
"Sometimes football is strange. I am disappointed for [Sunderland manager] Gus Poyet because they played well at the beginning and had some good chances. It was an unlucky own goal and maybe at 2-0 they should have had a penalty but after that we deserved to win.
"I am proud of the ambition of the team. They are always fighting for more and we need that. I am proud of everyone, even those on the bench because we have such a long season. The clean sheet is important. We have a strong defence and a superb goalkeeper and you have to look at the attackers when we don't have the ball because it is superb organisation."
The win was Southampton's fifth of the season and came on the back of Koeman's Manager of the Month award.