First team coaches Craig Shakespeare and Duncan Ferguson led the travelling party that left on Wednesday without Allardyce, who was appointed as the Merseyside club's boss last week.
Everton, who are already been eliminated from the Europa League with one point from five Group E matches, have one eye on Sunday's Premier League trip to local rivals Liverpool.
Allardyce has already confirmed he will field a makeshift team on Thursday with the Merseyside derby the priority.
Assistant manager Sammy Lee has remained at their Finch Farm training ground to work with the players who have not travelled to Nicosia.
Everton are without a win in 17 consecutive league games against Liverpool at Anfield, since a 1-0 victory in September 1999 courtesy of a Kevin Campbell goal.
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