The Black Stars think the decision to award the points to the Chipolopolo gives the Southern Africans the unfair advantage as they fight for one of the tickets to the 2014 World Cup in Brazil.
Zambia were third in Group D prior to the ruling on three points, level with second placed Ghana and one less than Sudan after two matches played.
On the back of the FIFA ruling against Sudan, African champions Zambia are now top of their qualifying group for Brazil 2014 on six points, three more than closest rivals Ghana.
Sudan are furious over the award of three boardroom points to Zambia insisting FIFA or CAF did not notify them of defender Saifeldin Ali Idris suspension as required by law.
Their view is shared by players of the Black Stars who think the field must be level for all countries as the fight to on the pitch to get point represent African at the World Cup.
Then in June, the two-time World Cup representatives in 2006 and 2010, travel to Khartoum to play the Nile Crocodiles in the return leg before a visit to Lesotho.
Sudan featured Saifeldin in a 2-0 win over Zambia in a Group D qualifier on June 2 in Khartoum.
Saifeldin was earlier suspended in his last competitive match prior to that game following his sent-off at the 2012 Africa Cup in a 3-0 quarterfinal loss Zambia on February.