Brown, who received the ban after being red carded for a fly kick at Neymar during Celtic's match against Barcelona on October 1, made a personal appeal for his punishment to be at a hearing at UEFA's headquarters in Switzerland.
The ruling means that Brown will miss the Ajax match in Amsterdam on November 6 and AC Milan at Parkhead on November 26.
Brown received an automatic one-game ban following the red card, which was then extended to three matches by UEFA's Control and Disciplinary Committee.
Celtic manager Neil Lennon said: "It has been turned down. We didn't win the appeal. It is disappointing. We thought we had a good case.
"He will be flying back and meeting up with the squad tonight.
"I feel the ban is excessive for a misdemeanour, or whatever you want to call it.
"I am sure we had a fair hearing but it wasn't to be.
"It is a blow for us and for Scott and we will just have to deal with it.
"You are hoping to have the ban reduced but if not, you have contingency plans just in case.
"We do have an idea of who will play there on Wednesday.
"We will have to keep an eye on Beram Kayal, we can't afford to lose too many players in that area because it is a crucial part of the pitch."