The Saints will not feature in the group stage of the prestigious European competition after getting knocked out by FC Midtjylland in the playoff round.
Premier League outfit Southampton played out a 1-1 draw with the Danish champions in the first leg of the tie at St. Mary’s Stadium last week.
On Thursday evening, the Saints suffered a 1-0 defeat to Midtjylland in the second leg of the tie away from home in Denmark.
Southampton have also made a disappointing start to their Premier League campaign.
Ahead of this weekend’s round of matches, Koeman’s side find themselves third from bottom in the league table with two points from three matches.
Saints manager Koeman, though, is not losing hope and has posted the following message on Twitter:
There is one direccion to chance the dificult start in the season! Why we had a fantastic last season? Focus and Teamspirit!! #WeMarchOn— Ronald Koeman (@RonaldKoeman) August 28, 2015
Direction? Thank you— Ronald Koeman (@RonaldKoeman) August 28, 2015
Southampton will take on Norwich City at St. Mary’s Stadium in the Premier League on Sunday.