Southampton have drifted away from the running for a UEFA Champions League place in recent weeks after three wins in their last eight matches, leaving them six points behind fourth-placed Manchester United.
And if they are to earn a place in Europe next season, Koeman believes they must win their next three matches, starting at Goodison Park on Saturday.
"Realistically it will be difficult [to make fourth]," said the Dutchman. "We have a distance in points, but if we win the next two or three we can fight for that.
"I think it is more for the bigger teams, but we'll try. The season has been fantastic, if we reach a European place it would be a special one for the club.
"But it's a tough test [against Everton]. They deserve a higher position in the table."
In contrast to Southampton's challenge at the top of the table, Everton have struggled in the league and only pulled away from the danger zone thanks to wins over Newcastle United and QPR prior to the international break.
Goodison Park has not been the fortress it once was this term – Everton have won just four games on home soil in the Premier League - and Martinez knows making that five will be no easy task.
"We are facing a difficult side at the weekend, for me they are the revelation of the season," said the Spaniard. "It is a great opportunity for us to focus and be ready for such difficult opponents.
"They are a really strong side, well-structured and creative with forward play. They have got the best defensive record in the league. That is why they are so competitive.
"Ronald Koeman has done a sensational job."
Everton recorded a 2-1 victory in this fixture last season thanks to Romelu Lukaku's late winner, but Southampton have won both games since without conceding a goal.
The reverse fixture at St Mary's Stadium in December saw a comfortable 3-0 win for Koeman's men, and started a run of six games without a win for Everton.
Martinez will run late fitness tests on Lukaku and Darron Gibson, while Kevin Mirallas and Stephen Pienaar are ready to be involved.
Midfielder Steven Davis is the only new injury concern for Southampton after returning from international duty with Northern Ireland with a groin problem.
