Everton were comprehensively beaten 4-0 by United at Old Trafford on Sunday, a result which condemned Koeman’s side to a fourth successive defeat in all competitions.
Toffees 8/11 to beat Bournemouth
Five of Everton’s close-season signings started the defeat, with one more – Sandro Ramirez – making an appearance from the bench in the second half.
Their transfer dealings are estimated to be in excess of £140m, a fact that led Mourinho to suggest in his programme notes that Everton should be looking to finish in the top four.
But that claim did not sit well with Koeman, who pointed to the first-season struggles of Henrikh Mkhitaryan as an example of some players needing a year to fully adapt.
“Every manager in life has doubts,” Koeman told reporters. “There is no one who has no doubts in football who is a manager.
“If you don’t win and you have a big number of players in your squad, you have doubts about the system. But that’s normal.
“I ask the question of myself. If Mkhitaryan gets one year to adapt to the Premier League, maybe I give my eight players one season to adapt.
“It was nice because I read the programme of United, and my colleague [Mourinho] talked about Everton and spending £140million and that we need to go for the top four.
“Sorry, but if there’s anybody who sees something in here [Mourinho’s claim] that is realistic and is possible for this Everton, please come up.
“Be realistic. Let’s talk at the end of the season. I’m not happy with how we started the season, but please be realistic about Everton.
“It starts with everybody; fans, press – we need time.”