Ronald Koeman pointed to a disallowed goal and an alleged handball in his assessment of Southampton's 2-1 aggregate defeat to Midtjylland in the Europa League play-offs.
A goal from Morten Rasmussen was enough to give Midtjylland a 1-0 second-leg win in Denmark, ending Southampton's European campaign after just four games.
Koeman said: "We were unlucky because in both games we were the better team. We had the most chances in both games.
"We scored a good goal at home that was not awarded by the referee."
A second-half James Ward-Prowse free-kick appeared to strike the arm of Rasmussen, and Koeman felt the striker should have been punished, saying: "The handball from the free-kick had an effect on the final result.
"We worked very hard but sometimes you need good and right decisions and we didn't have that."
Rasmussen's well-taken goal came after Jay Rodriguez lost possession near his own penalty area, leading to criticism from Koeman.
"We started very well. We created some good chances in the first 15 minutes," Koeman said.
"Jay lost the ball in a position where he can't lose it. One chance and it's 1-0 - very clinical and good from Midtjylland, but the final result was not what we showed on the pitch."
Senegalese attacker Sadio Mane, who is said to be the subject of interest from Manchester United, spent the entire game on the bench due to a hip problem.
Koeman defended his decision not to bring him on.
"Sadio wasn't 100 per cent. It will be a long season. I didn't take that risk because we need him for more games this season," he said.