The Dutchman was sacked as manager after 16 months in charge after the 5-2 home defeat to Arsenal left the Toffees languishing in 18th place in the Premier League.
Koeman, who has now been replaced by Under-23s boss David Unsworth on an interim basis, spent extensively in the summer but lost star striker and top scorer Romelu Lukaku to Manchester United.
And the 54-year-old believes it was the failure to adequately replace the Belgian, specifically with Arsenal's Olivier Giroud, was the precursor of what was to come.
“I had Olivier Giroud in the building. He would have fitted perfectly, but at the very last moment he decided that he’d rather live in London and stay at Arsenal," he told the Daily Mirror. “That was really hard to swallow. You tell me, where you can get a better striker?"
Koeman also points to his team's tough opening fixture schedule where they face five of last season's top six as another key factor behind the slow start that ultimately cost him his job.
“I looked at it and saw that five of our first nine games would be against clubs from last season’s top six: Chelsea, Tottenham, Man City, Man United and Arsenal," he added. “I looked at it again and I said to myself, 'Phew!'
"That is not going to be an easy run, in particular with a Europa League run at the same time and a really early start with all the players because of the European games. And most of all, because I had lost my striker Lukaku.’’
Koeman's successor Unsworth is the bookmaker's favourite to take up the job on a permanent basis and revealed following the 2-1 defeat to Everton on Wednesday evening that he is set for talks with owner Bill Kenwright on Friday to discuss his future.
“I honestly don’t know,” Unsworth replied when asked what sort of criteria he had been set. “All I know is that we’ll hopefully be as committed as that every game that I’m in charge. There’s an awful lot to work with there. It’s a very proud performance tonight.
“I’m scheduled to meet [Kenwright] on Friday afternoon. I speak to the chairman three or four times a day. The communication is brilliant. I’ve got a great relationship with the board. What will be will be. There’s no points return or games total that they’ve set. I just have to be committed. We have to try to win some games and take it from there.
“What has happened has happened, and it’s in the past. I can only influence the training sessions we’re going to be involved in and the games moving forward. I wouldn’t want to comment on what’s gone before, that’s history.”
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