Instead, assistant Craig Shakespeare and first-team coach Duncan Ferguson will take charge of a youthful-looking team.
With both sides already eliminated, the only issue riding on the tie is who will finish bottom in Group E.
And with a daunting trip to Anfield to come on Sunday, it’s no surprise that thoughts are already beginning to focus on that game.
The Daily Mail reports that Allardyce is missing the game due to a medical appointment arranged before he was appointed Toffees boss.
The Guardian meanwhile tells it as it is - that Allardyce is staying at Finch Farm to focus on the Merseyside derby.
Allardyce has already confirmed that McCarthy will get some playing time in Cyprus, and it’s likely that Davy Klaassen and Sandro Ramirez will get to play as well, alongside youngsters like Nikola Vlasic and Beni Baningime with Morgan Feeney.
The Liverpool Echo reported this morning that youngsters Harry Charsley, Nathan Broadhead, Alex Denny, Fraser Hornby and Michael Collins will be in the squad to Cyprus.
Everton fly out to Nicosia on Wednesday and spend two nights in Cyprus before returning to the UK on Friday.