The Eredivisie champions were too strong for their Cypriot counterparts in Amsterdam as they secured third place in Group F thanks to a Lasse Schone brace and further goals from Davy Klaassen and Arkadiusz Milik.
It ensures Ajax will feature in the Europa League next year and, while Ajax were comfortable in the end, they were made to wait until the stroke of half-time for Schone to edge them in front.
Two early second-half goals sent Ajax well on their way before the dangerous Milik capped off a resounding win.
De Boer was pleased with the way his side showed patience before the break.
"In the first half we didn't really manage to but in the end we broke them down, that's a great compliment to the boys," he told NOS.
"We were surprised by their way of playing. For APOEL only a victory was enough but they had 11 men standing in their own penalty area.
"It's too bad we did not keep the pressure on Paris Saint-Germain [in second]. Third place is alright but we would have liked to spring a surprise.
"We will be prepared for what's to come in the Europa League, but it makes sense that we want to get far as possible.
"We want to go far. That is clear. I have no preference for who we are given [in the Europa League]."
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