First-team coaches Craig Shakespeare and Duncan Ferguson will lead the Toffees against Apollon Limassol after it emerged Allardyce could not make the trip to Nicosia.
The 63-year-old, who was appointed manager last week, has remained at home as he has a pre-arranged appointment to attend.
Assistant manager Sammy Lee has also not made the trip and will work with the players who have been left behind for the dead rubber.
Everton are to field a weakened line-up after a dismal Europa League campaign which has seen them pick up just one point from their five group matches.
The hosts, with just three points to their credit, cannot qualify for the last 32 either.
Allardyce’s arrival has coincided with the departure of Joe Royle as professional development co-ordinator.
The former Toffees player and manager returned to the club in July 2014 under then manager Roberto Martinez with a brief to facilitate the progress of young talent from the academy as well as assisting in the scouting and recruitment of young players.
“I have thoroughly enjoyed my time at the club over the last few years and, in particular, the opportunity to work so closely with David Unsworth (the under-23s coach who stepped up to interim first-team manager after Ronald Koeman’s sacking),” he told evertonfc.com.
“I’ve been hugely impressed with the way in which he has developed his players – I’m certain he has a very bright future ahead of him.
“I would like to send my best wishes to Sam Allardyce and the club’s new coaching team, I’m sure they will guide us back to where we belong.”
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