Goals from Ricardo Kishna, Lasse Schone and Anwar El Ghazi saw Ajax inflict a first home defeat of the season on PSV, cutting the latter's lead at the top of the Eredivisie to 11 points.
Having held the lead for 48 minutes at Philips Stadion, De Boer's side found themselves pegged back with 11 minutes to play as Luuk de Jong netted for the hosts.
Two late goals ensured Ajax secured victory, but De Boer feels improvement will be required if they are to make any further dents in PSV's lead.
"I'm not expecting PSV, 11 points ahead, to have problems," said the head coach. "Especially if they play at the same level as they did on Sunday.
"We're obviously going to try to make it difficult for them. The spirit is good, that's a start. We now need to improve our game.
"It was a good lesson for the team. I'm pleased with the points, but not with the second half. After the break, we were mediocre.
"In the second half, we took a step backwards in terms of our play. PSV was making much better decisions; we were barely able to glean any opportunities.
"Based on individual class and luck, we happened to win. We didn't necessarily deserve it, especially as I didn't see much Ajax after the break."
