The Ajax coach was disappointed with his player's first-half display at the Bernabeu, but said he could not fault their efforts this term after they secured third place in Group D
A solitary goal from Derk Boerrigter was merely a consolation effort, in a game which proved too tough for the Eredivisie side.
"I was very, very mad at half time," De Boer told reporters.
"In these kind of matches you have to exceed your normal level. In my opinion there were nine players that were under their normal level.
"Only [Danny] Hoesen and [Kenneth] Vermeer were okay. If it's 2-0 at half-time you can consider us lucky. After half-time we played with more courage. I'm glad we scored, but maybe we could have scored one more."
Fury aside, the Dutchman acknowledged his side's achievement of finishing third in a group which was dubbed the toughest in this year's Champions League.
He added: "We can be proud of what we did. Becoming third in this group is a great effort by our team. A lot of people wouldn't have expected this, so that's worth a compliment.
"To become better, we have to play more matches at this level."