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."
"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."
