The South Africans claimed they were handed a raw deal by Senegalese referee Maguette Ndiaye, his assistants Samba Elhadji Malick and Camara Djibril after losing 1-0 to Ghana and missing out on the playoffs.
However, SAFA has attempted to paint a gloomy picture, making several frivolous claims against the Ghana FA - which has turned out to be a complete imagination and fabrication.
They even claimed ball boys were against them at the Cape Coast Stadium and want a review of the match and replay.
But the Ghana FA has warned the South Africans that they stand no chance against the African giants.
"The Ghana Football Association call on the South African Football Association to responsibly accept defeat and show respect to the Black Star’s achievement on the field, for this is not the first time Ghana has defeated South Africa and this will not be the last time. In fact, every South African knows the pedigree of the Black Stars in football, a reason the team has a lot of following in South Africa. The GFA will continue to project the positive image of football and protect the integrity of the game across the globe." part of an FA statement read
"The GFA wishes to state clearly that we will always operate within the FIFA Regulations and focus on our next match which is a play-off against any of the qualified teams we may be paired against.
"As a good sporting Association, we know that Bafana Bafana gave it their all but lost to a better team (and must be forthright to tell the South African public this). We wish Bafana Bafana and our colleagues at SAFA better luck next time.
Ghana reached the African World Cup play-offs courtesy of their win.
The match-defining moment took place in the 32nd minute when Ghana's Leicester City midfielder Daniel Amartey fell to the ground in the penalty area following a contact from South Africa defender Rushine de Reuck.
Andre Ayew tucked the resulting penalty kick to ultimately dump South Africa out of World Cup contention.
The Ghana FA has come out with all guns blazing against the South African Football Association (SAFA), saying the latter was "shocking and disrespectful" in how it portrayed the events that transpired in Cape Coast on Sunday.
In a tersely worded statement, the GFA said it was "shocking, irresponsible, and outright disrespect to note that our colleagues from South Africa Football Association have chosen to spread falsehoods to the media rather than project the real picture of events before, during, and after the game".