With eight games of the season remaining, the Saints are sixth in the table, six points adrift of Manchester United in fourth.
Dutchman Koeman remains upbeat about his side’s chances of qualifying for Europe, but knows the Europa League is a more realistic possibility.
“Realistically the Champions League will be difficult for us because we have the distance to make up in points,” Koeman said ahead of Saturday’s trip to Everton.
“If we win the next two or three games we’ll be fighting for it, but the Champions League is more for the big teams.
“We play eight finals now and the season so far has been fantastic. If we reach Europe, it will mean a special season for the club.”
On the trip to Goodison Park to face an Everton side who have endured a difficult season but have won their last two matches, Koeman added: “Everton are a tough test because they deserve to be in a higher position in the table. I like the way they play football and how Roberto Martinez is doing his job.
“They won the last two games and are playing with more confidence. It will be a tough game, but a nice one because we play the same way.
“How we play is about winning, not about controlling and defending. That makes the game more open than normal.”