It all started so well for Koeman's side with Wayne Rooney scoring the winner against Stoke City on the opening weekend before a draw at Manchester City.
But four consecutive defeats to Chelsea, Tottenham, Atalanta and Manchester United saw the Toffees concede 12 goals without reply to put them in the Premier League bottom three and facing an uphill battle in Europe.
A 3-0 victory over Sunderland in the Carabao Cup and a 2-1 comeback win over Bournemouth came at just the right time with Koeman under mounting pressure.
But more disappointment in Europe saw the Dutchman public question his players leading to further speculation he may not be around at Goodison Park much longer.
Koeman's claim that his players are 'scared to play' came ahead of today's visit of Burnley.
And former Premier League star Danny Mills told Sky Sports' The Debate that very public flogging had all the hallmarks of tactics often employed by Red Devils boss Jose Mourinho throughout his career.
"I think we've seen Mourinho do this sort of thing in the past where suddenly you support your players and support your players and you know what I've had enough, I've put my arm around you, I've given you as much confidence (as I possibly can) in the dressing room and it's not really working, so actually I'm going to play it a different way and out you a little bit and see if I get a reaction that way'," Mills told The Debate.
"Maybe the players aren't hearing him, aren't listening properly to what he's saying and he feels that he has to go out in the media and say 'Look actually if I say it in the media they will hear it' because they're all going to listen to it, it will get brought up, and if they are playing with a bit of fear they start going 'Actually yea, maybe he's right'.
"Yes it will hurt but I think he's hoping that that little bit of hurt in the media will make them go 'Well actually I don't want this getting any worse, we want this as a group to get better'."