Koeman: Top-four finish for Saints unrealistic
Southampton went into Saturday's clash knowing a point would be enough to lift them into fifth following Liverpool's 4-1 loss at Arsenal.
Despite dominating proceedings, however, they were overcome by Phil Jagielka's scrappy first-half goal, and Koeman conceded that his side - eight points off the UEFA Champions League places - must now focus on a push for Europa League qualification.
"You never know, everybody has difficult games to play, but it's not realistic at this moment to think about the top four - it's more realistic to think about the Europa League," he said.
"It's difficult now, because of the start we had, that teams are now playing differently against us, even at home - that's out of respect but it makes it more difficult.
"We have to find the different ways of getting around that, and we keep going until the end of the season, because getting into the Europa League would be a great achievement."
The visitors made a flying start at Goodison Park, with Tim Howard denying Graziano Pelle an early goal with a fantastic save.
But it was the hosts who went ahead when Leighton Baines' corner fell to Gareth Barry - the midfielder teeing up Jagielka, who duly nudged home.
James Ward-Prowse twice went close before the interval, but Everton held on for a third consecutive league triumph despite showing little attacking intent in the second half.
"We had a great start and a good chance from Pelle – it was a great save from Howard," continued Koeman.
"We had some good chances in the first half after that. I think the second half was more difficult because they dropped back, but they played really well with a really organised defence.
"I'm disappointed with the result but not about the performance of the team, we tried everything until the last second but it wasn't enough.
"It's frustrating because we deserved more, but that's football."