The Dutch coach bemoans poor first-half performance and admits that his side did not deserve anything from the match at the Amsterdam ArenA
The Dutch champions have lost both of their Uefa Champions League matches and speaking to French television network Canal+, De Boer expressed his disappointment in the performance.
"We have played quite badly. We have not reached our [best] level and when you don't, you cannot win against Madrid," he said.
"I'm disappointed, especially with the first 50 minutes. When it was 2-1 we created a bit more danger but we have not deserved to draw."
In his post-match conference, De Boer explained how his players paid too much respect to Jose Mourinho's side and lost the tactical battle.
"We had to play solidly when we didn't have the ball and search the spaces when we did have it. We didn't do either and that's a shame," he explained.
"I always say to the players that you must respect your opponent, but you should never worship them.
"That's something we did today and in that way you can never win against a team like Real."
The former-Barcelona defender also stoked the fire ahead of El Clasico on Sunday by confessing that he preferred the attacking tiki-taka of the Catalan club but could not help but admire the transition of Madrid's play.
"I view Madrid and Barca at the same level. I prefer to watch Barcelona for their style of play, but the transition of Madrid makes them very dangerous," he explained.
Ajax face Manchester City next in desperate search of three Champions League points at the Amsterdam ArenA on Wednesday, October 24.