Given the former England captain's recent seasons with Manchester United, it was unrealistic to believe he'd slot in at Goodison Park and replace Lukaku's goals, despite a promising start.
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.
Few would have expected Koeman's name to feature highly on the "managers at risk" list after the club's spending spree in the close season which saw players such as Gylfi Sigurdsson, Davy Klaassen and Michael Keane arrive for big fees.More news: Jose opens the door to potential Old Trafford return for Rooney
Bookmakers Ladbrokes have made Dutchman Koeman their new favourite to be sacked.
Ahead of the game this weekend, Mourinho claimed in his program notes that the Merseyside club would be aiming for nothing less than a Champions League place after they spent heavily during the summer.
Rooney went off with Everton a goal down and they finished the game conceding four in total.
Everton gamely hung on until Kevin Mirallas came on for Rooney, who left the pitch to measured applause from United fans.More news: The The Carrizo Oil & Gas, Inc. (CRZO) Bonds Trading 1% Lower
"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".
"He was clever and we need more players of that because he did every decision".
"Be realistic. Let's talk at the end of the season".
Amongst their Premier League rivals, Brighton and Hove Albion's last game without an academy player was 2016, while Bournemouth and Huddersfield's was only earlier this year.More news: Florida asks: When will power and AC be back?
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