Early strikes from Siem de Jong and Danny Hoesen seemed to put the visitors in control at the Koning Willem II Stadion before Aurelien Joachim and Genaro Snijders brought the hosts level.
Niklas Moisander (72) and Jody Lukoki (87) saw Ajax to victory, but De Boer, whose side are third, a point behind leaders PSV, was far from impressed.
“If you come here and lead 2-0, you expect to walk away 5-0,” he told reporters. “To throw away a lead like that simply cannot happen.
“It can cost you points. We made it difficult for ourselves.”
Moisander conceded the performance was from perfect, but with the top three so close, believes it was more important to get the win.
“It was not always good, but the three points are the most important,” he said.