Koeman, however, said his targets were unchanged from his debut season at the club when Everton finished seventh and that he needed more time before they could push for a top-four place.
"Is there anybody who sees this as realistic for Everton? Please, come on. Fans, press - we need time," Koeman told British media.
Everton are in the bottom three after losing three Premier League games in a row, conceding nine goals without reply. They also lost 3-0 to Italy's Atalanta in the Europa League last week.
"When you look at the fixtures at the start of the season, we knew we wouldn't win them all," Koeman said.
"We have played Manchester City, United and Chelsea away, plus Tottenham at home. Four title contenders, with the Europa League in between."
Everton's next league game is at home to Bournemouth, one spot below them in 19th, on Saturday.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Peter Rutherford)
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