The Ukrainian giants, quarter-finalists last season, started this season's campaign with a 2-1 defeat away to Porto.
And the fact the Nicosia side scored two goals in the space of three second-half minutes to see off Zenit St Petersburg in their own opener means Wednesday's match takes on new significance for Shakhtar.
Coach Mircea Lucescu is certainly not underestimating the threat of APOEL, as he said: "I would like to stress one more time that they are a Brazilian and Portuguese side, rather than Cypriot.
"There is a great climate and beaches in Cyprus - and APOEL's players work comfortably, without any pressure.
"But they do it at the top level professionally. I have seen them play and been greatly impressed.
"That's why I have told my players that the opposition is Cypriot only by the name, with the rest being entirely different."
He added on his club's official website, www.shakhtar.com: "In my opinion Zenit were not ready for their match against Apoel, and I would wish that we don't make the same mistake tomorrow [Wednesday]."
Lucescu ruled out a return for midfielder Fernandinho, who is still fighting for fitness after breaking a leg a year ago.
APOEL striker Ivan Trickovski believes avoiding defeat is the name of the game for the Cyprus League leaders on Wednesday.
The 24-year-old Macedonia international explained: "We know Shakhtar are a very good team with a glut of class players.
"However, we will do our best to play to our full potential in order to receive an acceptable result."
Goran Popov has compared Trickovski to Shakhtar's Andriy Yarmolenko, who is tipped for a big future in the game at the age of 21.
Trickovski, linked with summer moves to Rangers and Sochaux, added: "I thank him for the kind words. It's a nice comparison as Yarmolenko is a very good football player.
"I'm constantly working on my game and always look to improve as a player."