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"We have evaluated the situation and we came across the issue that we made a mistake," said Sahlu Gebrewold, chief executive of Ethiopia's Football Association.
"We accepted the allegation that this was inappropriate.
"There won't be an appeal from us being lodged."
Ethiopia are now almost certain to be docked three points, meaning South Africa would get a reprieve and may still be able to qualify for the 2014 finals in Brazil.
FIFA match records have also confirmed that Togo, along with Ethiopia have fielded suspended stars in 2014 World Cup qualifiers during June.
Midfielder Manyahile Beyene played for Ethiopia in Botswana instead of serving a one-match ban having been cautioned in Group A games away to South Africa and at home against Botswana.
Another midfielder, Alaixys Romao of Togo, committed a similar offence, starting in a Group I home game against Cameroon when he should have been sidelined following cautions in two earlier matches.
World football governing body FIFA issued a statement last weekend saying they were probing games involving Togo, Ethiopia and Equatorial Guinea over the alleged use of ineligible players, but did not name them.
The standard punishment for a team guilty of using an ineligible player is that their opponents are awarded a 3-0 victory, with Sudan, Burkina Faso and Gabon already punished during the 2014 qualifying competition.
Sudan played suspended Eldin Adris, Burkina Faso used Cameroon-born Herve Zengue, and Gabon picked Charly Moussono, who represented Cameroon at the 2006 Beach Soccer World Cup.
Should Togo, Ethiopia and Equatorial Guinea be found guilty, it would have a major impact on three groups with eliminated countries South Africa and Botswana (Group A) and Cape Verde Islands (Group B) coming back into contention.
Cameroon, who trail Libya by two points with a home fixture against them to come during September, would take a one-point advantage, leaving them needing a draw to reach the play-offs.
The matches being investigated are Togo 2 Cameroon 0 on June 8 in Lome, Botswana 1 Ethiopia 2 on June 7 in Lobatse, and Equatorial Guinea 4 Cape Verde Islands 3 on March 24 in Malabo.
On Tuesday, FIFA said in a separate statement they were also probing whether Equatorial Guinea contravened the competition regulations when they lost the return match against Cape Verde 2-1 on June 8 in Praia.
An undisclosed decision was reached by FIFA regarding the Equatorial Guinea-Cape Verde game in Malabo, but the part-island state must have been found guilty as they lodged an appeal.
It does not appear yellow card-related as match reports show Ben Konate was the only Equatorial Guinea player to receive two cautions and he served a one-game suspension.
A probable cause of the probe is the use of foreign-born players by the Equatoguineans with the side that started against Cape Verde including no footballer born in the country.
Five were born in Brazil, three in Spain and one each in Ivory Coast, Liberia and Ghana. Malabo-born Konate was among the three substitutes used with the others born in Brazil and Colombia.
FIFA rules state that if a footballer is not born in the country he wishes to represent, a parent or grandparent of his must have been born there, or he must have lived there continuously for at least five years.
Respected London-based magazine World Soccer has regularly reported that some players fielded by Equatorial Guinea, who co-hosted the 2012 Africa Cup of Nations and reached the quarter-finals, meet none of the criteria.
