South Africa failed to qualify for the World Cup play-offs after losing 1-0 to Ghana in Cape Coast last Sunday.
A first-half penalty from Andre Ayew was enough to separate both teams after Daniel Amartey went down following a challenge from De Reuck.
The penalty, which was awarded by Senegalese referee Maguette Ndiaye, has since been contended by South Africa FA.
On Monday, SAFA announced that it had lodged a complaint at FIFA to have the match investigated and possibly replayed.
The Association also organised a press conference on Wednesday, where they alleged match-fixing, match manipulation and bemoaned other decisions they felt directly influenced the game.
However, reacting to this in a statement released on Thursday morning, the GFA took exception to the allegations, referring to them as frivolous and baseless.
“We wish to state categorically that the allegations are frivolous, baseless and lacks merits and should be treated with all the contempt that it deserves,” a section of the statement said.
“These allegations from South Africa Football Association are nothing but a planned scheme and a calculated attempt to shift focus from the defeat, divert attention from their failure to qualify for the play-offs and unjustly dent the hard-earned victory of the Black Stars.”
It added: “The Ghana Football Association will not allow the SAFA to visit its incompetence on it through these allegations… 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.”
Meanwhile, FIFA has acknowledged receipt of SAFA’s complaint, saying investigations are ongoing into the allegations.