The decision means that if forward Ronaldo, the world's most expensive player, receives a yellow card against North Korea on Monday he will be suspended for Portugal's final Group G game against Brazil four days later.
"We have been told by FIFA it has rejected the appeal. It said it was not an error of fact, which happens for example when the wrong player is booked, and was at most an error in relation to the rules," the spokesman told reporters.
"In these cases the referee is sovereign, so FIFA has rejected our appeal," he added.
Ronaldo and Ivory Coast right back Guy Demel clashed off the ball in Tuesday's 0-0 match and were both booked.
The Portuguese had asked FIFA to revoke Ronaldo's caution, alleging that he had been fouled by Demel and then surrounded and insulted by several Ivory Coast players.
Portugal midfielder Raul Meireles criticised FIFA's decision.
"Cristiano is an important player for us. It was a situation in which he did absolutely nothing and got a yellow, and it's that type of yellow card that hurts the most," Meireles told reporters.
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