A dip in form has seen the south-coast club pick up only four points from their previous five matches, yet Southampton remain sixth in the table and very much in the hunt for UEFA Champions League and Europa League berths.
Koeman was encouraged by the way his side responded to a previous blip in December, by winning five of their next six fixtures.
"I think the reaction of the players was fantastic after that and I expect the same reaction in the last 11 games," said the Dutchman in a news conference ahead of Tuesday's home game against Crystal Palace.
"We're still in a high position on the table. That's the focus for the players. If we win five of 11 games, that means 61 points and that means, in my opinion, European football.
"I still believe at the moment that we can finish in a high position on the league.
"If we win seven or eight of 11, maybe we will be fourth in the league, but I realise it's very difficult, because we have to beat some big teams."
Southampton's main problem in recent weeks has been a lack of goals, finding the net just once in their last five Premier League games.
Koeman acknowledges the need for improvement in the final third, but refused to single out striker Graziano Pelle, who is without a league goal since December 20, for blame.
"One of the reasons [for a lack of goals] is now they [opponents] know exactly the strengths of our team," Koeman added.
"Still we are creating chances, but maybe we need [to be] a little bit more ruthless in the box, more confident in the box. It's a team question, not an individual question of Pelle or another striker.
"We need everybody to do the last part of attacking in a better way than we did in the last few games.
"I don't like to focus on one player. He [Pelle] is working and doing everything we expect. It's a difficult time for him, but he's an experienced player and he has to show his qualities.
"And, of course, he has to score. Everybody knows that and, first of all, he will know that."
