A first-half goal from former Celtic striker Morten Rasmussen secured a 2-1 aggregate win – and with it a place in Friday’s group stage draw.
The Saints saw an early Jose Fonte effort cleared off the line but were then punished by Rasmussen’s angled shot following a Jay Rodriguez error.
Southampton rarely looked like getting an away goal to force extra time.
After finishing seventh in the Premier League last season, this was a disappointing end to Southampton’s first entry into Europe since 2004.
Ronald Koeman’s side eased past Dutch club Vitesse Arnhem in their first qualifying round but did not convince against Midtjylland in the first leg, drawing 1-1 at St Mary’s.
And apart from Fortune’s early chance and a blocked shot from James Ward-Prowse, they carried little threat on Thursday.
Rasmussen accepted a pass from Kristian Bach Bak to turn sharply and hit the 28th-minute winner after Rodriguez had been caught in possession.