Last Sunday the Toffees boss called for some realism in response to Manchester United counterpart Jose Mourinho's comment that Everton, having spent over £140 million during the summer, are a club who "wants to at least secure a top-four position this season".
Koeman, whose side are 18th in the table and suffered their fourth straight loss in all competitions when they were beaten by United, added that what he regarded as realistic was "the same as last season", when Everton came seventh.
Asked about those remarks as he looked ahead to Saturday's home clash with Bournemouth, the Dutchman told reporters: "I know what we are and I know the way to be successful.
"It's crazy, ridiculous to put a lot of pressure on the team by saying we need to finish in the top four. In my opinion, that's ridiculous.
"Everybody has signed new players. We signed some young players, and (on Wednesday, in the Carabao Cup win against Sunderland) we played with six or seven boys of 19, 20, 21, 22.
"That is the future, it needs time, and that is normal. Let's make the next step.
"It doesn't mean we don't have ambition, because if there's one person in football who has a lot of ambition, then it's at this table.
"But I'm realistic, and in football, being realistic is sometimes difficult."
When it was put to him that Everton are a club who traditionally give their managers time, Koeman said: "What I feel is really a good connection with the board, and we speak about football. I speak with (director of football) Steve Walsh about football, about the team.
"I think everybody knows the direction, and the difficulty there has been at the start of the season. But okay, it is football, and you need to win."