SAFA announced it would not appeal the order that annulled South Africa's 2-1 win over Senegal last November, but said that its "rights to sue for damages remain open".
The world footballing mother body made the ruling last week, which was based on the fact that the referee who officiated South Africa's 2-1 win over Senegal in November a year ago, Joseph Lamptey, has been handed a lifetime ban for match manipulation. SAFA senior legal counsel Norman Arendse said.
Federation Internationale de Football Association found neither team was involved in the fixing, and the referee was likely manipulating the match for illegal betting rings.
The world football governing body then told Safa they could not appeal the decision.
The Court of Arbitration for Sport also upheld the life ban for referee Lamptey.
As a result, the FBF accuses Federation Internationale de Football Association of deliberate favouritism and demands the decision be reversed in order to "save us from a referral to the Court of Arbitration for Sports".
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Burkina Faso top the group with six points, just ahead of island nation Cape Verde on goal difference, with only the group winners qualifying for the World Cup in Russian Federation. It should be rubber-stamped, with no opposition now from SAFA.
A statement on Tuesday said: "Following additional information SAFA received from world governing body FIFA, the Association resolved on moral and ethical grounds that we can not be beneficiaries of corrupt activities".
The game will be replayed in November, likely after all the other qualifiers in the group are completed.
South Africa are bottom of Group D with a point from three matches - four points behind Senegal, and five shy of Cape Verde Islands and Burkina Faso.
While FIFA's decision badly hampers South Africa's World Cup hopes, it gives Senegal a second chance.