The club have also been given a warning about a lack of stewarding.
The Dons had been charged with "crowd disturbances" and having no stewards travelling with their support, in contravention of Uefa regulations.
Aberdeen lost the third qualifying round second leg 2-0 in Cyprus, exiting 3-2 on aggregate.
Police Scotland confirmed no officers travelled with Aberdeen to Cyprus or to Bosnia-Herzegovina in the previous round against Siroki Brijeg, stressing that liaison officers are only sent at the request of the host nation.
Apollon have been fined £25,000 after being charged with improper conduct by their team, who received five yellow cards, and with the setting off of fireworks and throwing of objects by their fans.
The Cypriot club had used the AEK Arena in Larnaca for the tie against Aberdeen as their Tsirio Stadium is being redeveloped.
Riot police moved into the away section as Aberdeen fans clashed with stewards following the final whistle.
Flares had been lit early in the second half in the home section, with one thrown and landing inside the goal behind Aberdeen goalkeeper Joe Lewis.
Television cameras caught Swiss referee Stephan Klossner telling an official that he would abandon the match if the behaviour did not cease.