A first-half strike from Morten Rasmussen was enough to send FC Midtjylland into Friday's draw for the UEFA Europa League group stages, with Southampton's own continental adventure ending prematurely after just four matches.
Koeman was already unhappy having seen a Steven Caulker header chalked off in the first leg as FC Midtjylland left St Mary's with a 1-1 draw and he again questioned the decision not to award his side a penalty as it chased the tie in the MCH Arena.
James Ward-Prowse was furiously appealing for a penalty after claiming his free-kick came off an arm in the Midtjylland wall, with his manager not shying away from offering a scathing opinion on the officiating across the tie, which ended 2-1 on aggregate.
"I have to say, and it's critical to both referees in both games, if you analyse both games, we had more chances," he said.
"We scored a normal goal last week and if you watch television and you see the free kick of Ward-Prowse - it's a penalty. So easy. But if you don't see it that still makes it more complex, more difficult.
"Then the final result, the final result of last week, is totally different (if the decisions are correct). Congratulations to Midtjylland. They play well, they play out of a good organisation and they scored today and we didn't.
"It's two mistakes. It's one penalty and one goal and it's a big influence on the result. It's different reasons. One of the reason was the referee of today because it's a penalty. Last week it's a normal goal but we did a mistake and they scored a 1-1.
"Not all (blame) goes to the referee, that's too easy, but a part of our disappointment and the final result is also by the referee."
Koeman conceded his side lacked a creative edge and insisted Sadio Mane, a transfer target for Manchester United, did not come off the bench as he did not want to take a chance on the Senegal international's hip injury.
"We had the experience about last week it's difficult because they defend well," he added.
"One of the qualities of them is aggressive winning second balls and then you need to be more creative.
"I think Dusan (Tadic) came in the game and he makes the difference but in the process not lucky enough. Every ball fell to one of them.
"Sadio wasn't 100 per cent and I didn't take the risk because it's the start of the season. It's not everything today."
Jay Rodriguez was at fault in the build-up to Rasmussen's decisive goal as he conceded possession on the edge of his own box to allow the ex-Celtic forward to turn Jose Fonte and fire past Maarten Stekelenburg to score with his side's first decent chance of the game.
When asked how disappointed he was with its European exit, Koeman replied: "Very, because if you don't create chances the disappointment is a little bit different.
"I think we start well the game, we dominate the game, we had some good chances in the beginning and one mistake, one chance, very clinical 1-0.
"But congratulations to Midtjylland. They play well, they play out of a good organisation and they scored today and we didn't."
