The Dutchman was visibly irked by the suggestion made by Jose Mourinho in his programme notes ahead of last weekend's clash between Manchester United and Everton that the Toffees should be aiming to end up in the Champions League places because of the money the club spent over the summer.
Everton shelled out what could end up being around £140m on new players during the last transfer window once appearance-related add-ons are factored in but, after recording an opening day-victory against Stoke and almost beating Manchester City at the Etihad Stadium, they have lost three Premier League games on the bounce without scoring a goal.
While Koeman expects his side to improve now that a difficult run of fixtures to start the new season is out the way, he used the occasion of his pre-match press conference before Saturday's clash with Bournemouth to restate his belief that this season is too soon to be talking about his young Everton outfit as a top-four team.
“Maybe it was different for everybody because we reached the Europa League [group stage]," he explained. "We had a good game at home and three points against Stoke. We had one point away against Manchester City that [made] everybody maybe expect much more [than] we have showed until now.
“I don't care. I know they (the press) have the easiest job in the world to analyse, to make columns but I know what we are. I know the way to be successful and it's crazy… it's ridiculous to put a lot of pressure on the team by saying we need to finish [with] the top four teams. In my opinion that's ridiculous.
“Everybody got time. Everybody signed new players. We signed also young players and we played yesterday with six, seven boys of 21, 20, 19, 22 and that's the future and that needs time and that's normal.
“Let's take the next step but that doesn't mean we don't have ambition because if there's one person in football who has ambition he's at this table. But I'm realistic and sometimes being realistic in football is difficult.”