The Dutch coach was disappointed with conceding a first-half spot-kick and believes his side should have triumphed at Celtic Park
The Dutch champions went down 2-1 in Glasgow, a result that leaves them rock bottom of Group H with just one point from three matches.
But De Boer says his side didn’t earn the result their performance deserved.
“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.
Stefano Denswil conceded a 43rd-minute penalty for a clumsy challenge on Anthony Stokes which James Forrest converted.
And the Ajax boss was left disappointed with the 20-year-old for handing the hosts the lead.
“We shouldn't give away penalties as easy as we did today,” De Boer continued.
"It's an unfortunate moment of Stefano Denswil because he's still very young, but as a defender you should not challenge like that unless you are 100 per cent sure you'll get the ball.
“Eight out of 10 times, the referee will blow for a foul."
Ajax have a chance for redemption next month when they continue their Champions League campaign by hosting the Scottish champions at the Amsterdam ArenA.