The Saints slipped to 13th following a 1-0 defeat by Norwich on Saturday after Victor Wanyama was sent off for a dangerous tackle in the second half, while Senegalese midfielder Sadio Mane was dropped from the starting line-up for missing a pre-match meeting.
Koeman's side have lost six of their last eight league games to sit seven points off the relegation places and the Dutchman is conscious they are now in a "difficult situation".
"We have to change some disciplinary things in the group because we need more focus. If you're not focussed, I can't manage a player," Koeman told the Southampton YouTube channel.
"It's the most difficult situation until now. Now we have to keep togetherness.
"That is what I expect and that is not what we showed (against Norwich) because that is against that message."
Southampton next face Crystal Palace in the FA Cup third round on Jan. 9 followed by home games against Watford and West Bromwich Albion in the Premier League, all in the space of seven days.
"Of course, we need points. It's not the position on the table where we like to be," added Koeman.
"We like to win -- that's the best medicine to get the confidence back and to get the mentality back."
(Reporting by Rob Hodgetts, editing by Pritha Sarkar)
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