Danish champions Midtjylland surged into the lead on the stroke of half-time through former Southampton academy graduate Tim Sparv before striker Jay Rodriguez scored his first goal since March 2014 from the penalty spot.
Southampton now face the tricky task of overcoming Midtjylland, whose majority shareholder is Brentford chairman Matthew Benham, on their own turf in next week’s second leg in order to make European progress.
“It’s not a very good result,” said Koeman. “We’re not really the favourites any more as they have a good result. We will fight for a win. Even a 2-2 draw would be good.
“We have to learn, they are a difficult side. We have to look to ourselves and learn and do things a better way next week.”
Finnish midfielder Sparv failed to make an appearance for Southampton before departing for Swedish side Halmstad in 2007 but fired past goalkeeper Maarten Stekelenburg moments before the break. But Rodriguez, who ruptured his anterior cruciate knee ligament in April 2014, levelled from the spot 11 minutes into the second half after James Ward-Prowse had been felled by Kian Hansen.