A FIFA statement said that the 31-year-old Real Madrid defender, who was red-carded for the incident, had been fined 15,000 Swiss francs (12,300 euros).
Pepe's arm caught Mueller during Monday's Group H match and the German fell to the ground grimacing. Pepe infuriated at what he considered Mueller's playacting then pushed his head onto the German's forehead and got an immediate red card.
Germany, already leading 2-0, went on to win 4-0.
Pereira kicked Costa Rica striker Joel Campbell towards the end of the game and now misses his country's crucial game against England on Thursday.
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