The four-time defending Eredivisie champions could have gone top of Group G – which also contains European heavyweights Barcelona and Paris Saint-Germain – with victory in Cyprus.
Lucas Andersen gave Ajax a short-lived lead in the 28th minute, only for APOEL to quickly level from the spot.
And De Boer felt Gustavo Manduca's penalty – awarded after Ricardo van Rhijn was penalised for handball – was not merited.
"That [penalty] was nothing," De Boer is quoted as telling NOS.
"We were Lord and master and got a penalty against [us] which [was] no penalty. We have also had opportunities to finish it off. Unfortunately we did not succeed."
Ajax piled on the pressure late but could not convert, Lasse Schone and Thulani Serero spurning good chances.
Despite the disappointing result, De Boer was still impressed with the way his side played.
He believes Ajax simply must progress in Europe - be it in either the Champions League or the UEFA Europa League.
"I'm satisfied how we've played," he added.
"If we continue, then [we'll win] points. That is possible against Barcelona. I think we are better than APOEL.
"Winter in Europe is a must. Preferably in the Champions League, otherwise in the Europa League."
