It was a season that began with much optimism after a positive transfer window but Koeman tried to play down expectations after Sunday's 4-0 defeat at Manchester United.
He seemed particularly frustrated by remarks from United boss Jose Mourinho in his program notes which suggested, after spending £140million, Everton would want "to at least secure a top-four position".
Koeman said: "I read the program of United and my colleague told about Everton, 'They are spending £140million, they need to go for the top four'.
"Sorry, if there's anybody in this room and outside who sees something realistic (about) what is possible for this Everton, please come on. Be realistic and let's talk at the end of the season."
He added: "I felt there was something possible this afternoon because I wasn't so impressed by United. That is maybe strange after a 4-0 defeat but they were really clinical and we didn't deserve this high defeat."