Bougherra netted in Algeria's 1-0 home win last week to give the North Africans an away goals victory in the two-legged playoff, which ended 3-3, and sent them to the 2014 World Cup.
"FIFA communicated to the Burkina Faso Football Federation that the formal conditions to lodge a protest were not met," soccer's world governing body said in a statement.
"Irrespective of the foregoing, FIFA also communicated that no breach of the FIFA regulations has been committed by the Algerian FA in relation to the matter at hand."
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Last week's match was full of controversy.
Senegalese referee Badara Diatta added on only four minutes of stoppage time after a second half which was continually interrupted due to treatment for the Algeria players.
He then blew the final whistle one minute early even though added time itself had also been interrupted for at least 90 seconds while another player received treatment.
Bougherra himself was lucky to stay on the pitch after a shocking flying tackle during the first half.
The African qualifiers were plagued by controversies over ineligible players and nine matches were forfeited by teams for breaching the rules, including Burkina Faso on one occasion.
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