National association president Danny Jordaan said Saturday in a statement that issues for debate could include appealing the decision, writing to FIFA or taking legal action.
He called the order to replay the match during the November 6-14 international window “devastating news that had stressed South Africans”.
South Africa defeated Senegal 2-1 at the group stage last November, but both their goals stemmed from controversial decisions by since-banned Ghanaian referee Joseph Lamptey.
The penalty that enabled South Africa to take the lead was awarded for a non-existent handball with TV replays showing the ball striking the thigh of a defender.
Later, Lamptey was ordering Senegalese players to retreat for a free-kick when it was taken and the home team increased their lead.
FIFA gave Lamptey a life ban for match manipulation and his appeal was rejected this week by Switzerland-baaed international sport judicial body CAS.
No details of who might have influenced the Ghanaian to fix the result have been released by FIFA.
Lamptey has a history of controversial decisions in national team and international club fixtures, including allowing a handball goal and playing suspiciously long periods of stoppage time.
The replay decision came this week after South Africa suffered home and away defeats by lowly Cape Verde within five days to diminish hopes of reaching the 2018 World Cup in Russia.
Burkina Faso and Cape Verde have six points with two matches to play and Senegal five and South Africa one with three games left. Only group winners qualify.
South Africa host Burkina Faso in Johannesburg on October 7 and must also play Senegal away during November.
Jordaan urged South Africans not to criticise FIFA general secretary Fatma Samoura, a Senegalese.
“We hold her in high regard as the first African to hold this senior post in our world football governing body,” he said.
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