After Everton's spending spree this summer, many could be forgiven for thinking they might make a large jump forward this season.
In the early going, it seemed like they might. They beat Stoke 1-0 and then gained a very creditable draw away to title favourites Manchester City.
However, since then, defeats to Chelsea, Tottenham and now Atalanta in the Europa League have started to raise concerns.
The Serie A outfit, who were playing on home soil, were comfortably the better side throughout and to be honest, the 3-0 scoreline flattered the Toffees.
Koeman had fielded a relatively strong side that featured the likes of Leighton Baines, Wayne Rooney, Michael Keane, Morgan Schneiderlin and Gylfi Sigurdsson, but he did make some changes with the likes of Dominic Calvert-Lewin and Mason Holgate pushed into the lineup.
After the game, the Dutchman took responsibility for the loss and posted an Instagram post (also on Twitter) explaining himself.
However, that wasn't enough for the Everton faithful.
Take a look at the responses the former Southampton manager was subjected to:
And they're just the ones we can show. To see the X-rated replied, click on the tweet.
Speaking to BT Sport after the game, Koeman was under no illusions that something has to change.
"I need to criticise myself because the team was not prepared for this tonight and that's a question to myself," he told BT Sport.
"They showed more aggression, they showed more passion."
"I asked myself questions on what I was doing wrong against Tottenham, because it's not how I like to see my team.
"We can play bad football, we can miss chances, but the commitment and passion Atalanta showed in the first half was much bigger than we showed."
"The whole team of Atalanta was better prepared than we were today," he said.
Things aren't getting any easier for Everton. Next up, they face a trip to Old Trafford to face Manchester United on Sunday with old striker Romelu Lukaku on fire already for his new club.
The Belgian already has five goals this season for the Red Devils; will it be he or Rooney who steals the show against their former club on Sunday?