"The appeals lodged by the Hungarian Football Federation and Bulgarian Football Union were both rejected and the decisions of the FIFA disciplinary committee are confirmed in their entirety," FIFA said in a statement.
"The MLZS and BFU have both been warned to their future conduct," added FIFA.
"Should such incidents of a racist/discriminatory nature occur again, the FIFA disciplinary committee would be left with no other option than to impose harsher sanctions, which could go as far as forfeiting a match, a points deduction, or disqualification from a competition."
Bulgaria were sanctioned after a group of supporters racially abused Denmark's Patrick Mtiliga every time he touched the ball after he entering the field in the second half of their World Cup qualifier in Sofia in October.
Hungary's punishment followed anti-Semitic chanting by fans in a friendly at home to Israel in August.
Bulgaria, whose next home game in Group B is against Malta in March, were also fined 35,000 Swiss francs (£24,000) and Hungary, who host Romania also in March in Group D, were fined 40,000 francs (£28,000).
FIFA said that during the Bulgaria match, also marred by a firework-throwing incident in the seventh minute, fans were warned by the stadium announcer about their behaviour in the 73rd minute.
FIFA said that in Hungary's case, it had been informed by the FARE (Football Against Racism Europe) group that some supporters had made anti-Semitic chants and displayed offensive symbols.
- Sports & Recreation
- Hungarian Football Federation
- Bulgarian Football Union