The Saints' stellar season has stuttered in recent weeks, largely due to their impotence in front of goal.
In their last 10 league matches they've scored just seven times, resulting in a haul of 14 points from a potential 30.
Still, though, the south coast side are punching well above their weight and sit seventh in the Premier League with 53 points from their 31 outings - one point behind Tottenham Hotspur in sixth and Liverpool in fifth.
European football is the goal and, starting with Hull City on Saturday, Saints have seven matches to chase that dream.
"You have to look at yourself and to do your best," Koeman said on Thursday. "You have to have the ambition, spirit and quality.
"We have a little bit more difficulty in creating enough chances to score and we have to work on that. Now the situation at the moment is that we are fighting for fifth, sixth and seventh position in the table and that's still very good.
"We have a home game now and if you want to finish up in the table you have to win games like this."
Saints have failed to score in five of their last nine league matches, and Koeman could be poised to recall Senegalese striker Sadio Mane to the starting 11.
Koeman is looking for his best attacking combination and with Graziano Pelle continuing to misfire, winger Mane could be called on to play up the middle.
"We need to have patience and we need to bring more quality in front (of goal). Then it's all about the performance," Koeman told the club's YouTube channel.
Hull are scrapping for their top-flight lives and will be tough to break down. The Tigers are one place above the drop zone, two points clear of Queens park Rangers and Burnley, and six above rock-bottom Leicester.
Chelsea lead the table with 70 points, ahead of Arsenal on 63, Manchester United on 62 and Manchester City on 61.
(Writing by Ossian Shine; Editing by Toby Davis)
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