After a 1-0 defeat by West Bromwich Albion on Saturday, Southampton have slipped to sixth in the Premier League table, four points behind fourth-placed Manchester United.
Former Saints boss Alan Pardew brings his resurgent Crystal Palace to St Mary's on Tuesday and Koeman is targeting victory after mapping out his squad's route to European qualification.
"Champions League football is still possible if we win seven or eight of 11 matches but it will be difficult," Koeman told a news conference.
"If we win five of 11 games that means 61 points and we will be playing European football.
"We had a difficult period in December and the players had a fantastic reaction. I expect the same."
Much of Southampton's early success was down to striker Graziano Pelle, who has scored 12 goals in all competitions this season, but the Italian has not found the back of the net since December.
Koeman backed the out-of-form Pelle to recapture his form and the Dutchman is aware his side need to be more clinical with their opportunities to keep pace with the top four.
"We need to be more ruthless in the box but it's not just the strikers, it's the team who need to create more chances," he said. "I need to be clear to the players in what we are trying to do and trying to reach.
"It's a difficult time for him (Pelle) but he's got the qualities. I know the player well and he needs support.
"I don't like to focus on one player. We need more players in a better shape in our attacking. Strikers live for goals."
(Reporting by Michael Hann, editing by Tony Jimenez)
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