The Merseyside club have endured a torrid start to the campaign despite spending around 145 million pounds (A$248 million) on transfers in the off-season.
They failed to score in their last three league games, which ended in consecutive defeats to Manchester United, Tottenham Hotspur and Chelsea and Koeman said the club must set realistic goals for the season.
"I know what I like and the way to be successful. It is ridiculous to put a lot of pressure on the team to finish in the top four," Koeman said ahead of their clash with Bournemouth on Sunday (AEST).
"Everybody signed new players. We signed young players. That needs time. Let’s make the next step. That doesn't mean we don’t have ambition. If there is one person in football (who is ambitious) then he is on this table - but I am realistic."
With a convincing 3-0 victory over Sunderland in the League Cup on Thursday (AEST), Koeman hopes Everton have turned a corner heading into the weekend.
"Now we have to show we are confident. Yesterday was the best medicine. Good performances usually bring winning games," he said.
Koeman said injured midfielder James McCarthy could return to training next week, while long-term injury absentees Seamus Coleman and Yannick Bolasie are ruled out until November.