Apoel started the game fiercely attacking their Lithuanian champion opponents FK Suduva to try and overcome a first leg 3-1 defeat that they suffered last week in Lithuania.
Michael Pote scored with a classic header in the 20th minute to give Apoel a 1-0 home lead.
They continued chasing the game with no avail hoping another goal would get them through on away goals but eventually lost 3-2 on aggregate.
The only consolation for Apoel is now they can play in the Europa League second round qualifying stage where they will face the winner of Flora Tallinn or HapoelBeer Shiva who have already played the first leg and Hapoel Beer Shiva are winning 4-1 on aggregate.