However, the 43-year-old claims that the scoreline did not accurately reflect the performance of his side.
"In football, the best team does not always win," he told NOS
"If you compare the chances of both teams, then we should have won tonight. We created some real chances and they did not."
The defeat leaves De Boer's charges bottom of Group H with slim hopes of progressing to the latter stages of the competition.
Ajax host the Scottish giants in Amsterdam in two weeks, before welcoming Barcelona to the Dutch capital on November 26.