The Dutch champions' head coach was not overly disappointed with the loss, as he felt his team put in a decent performance but were simply caught out by their opponents
The Eredivisie side started the match at Santiago Bernabeu brightly, but fell behind after a superb Real Madrid raid in the 25th minute and were unable to find a way back into the match thereafter.
"We saw a lesson in counter-attacking football tonight," De Boer said at the post-match press conference.
"We controlled the game well, but we had set a target to play on the counter-attack. I had already warned my team that Madrid were dangerous on the break and you have to be smarter than we were for the first goal.
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"We started well and could have taken the lead early on. After that we got taught a lesson in efficient counter-attacking football. Sometimes we are a bit naive.
"Our first objective was to play our own game. We did that in the opening exchanges. That should have eased some pressure from the players. However, if there is space behind you there is always a threat.
"Madrid have so much quality they are always dangerous and always likely to produce something on the break."
Ajax sit third in Group D with only one point from their opening two games, while Madrid sit top of the table with six points.
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