During the match against Egypt played at the Cornella, home of Espanyol, on March 31, part of the crowd chanted "whoever doesn't jump is Muslim".
On August 4, three weeks after Spain won the World Cup, FIFA's disciplinary committee imposed a fine of $20,000 (€17,800) and closure of at least 15 per cent of the stadium for Spain's next home friendly.
The RFEF reiterated on Friday that this misconduct "was detected by the Federation's own monitoring mechanisms" and that announcements urged the crowd to stop the chanting at half-time, during the second half and on the stadium video screens.
The RFEF said it had cooperated fully to help identify those responsible. It said it would appeal to the Court of Arbitration for Sport (CAS).
One of Spain's starters during the match, forward Lamine Yamal who plays for Espanyol's local rivals Barcelona and was born in a suburb near the Cornella stadium, is Muslim. At the time he called the chants "a lack of respect and something intolerable".
Spain manager Luis de la Fuente also called the chants "intolerable".
"Violent individuals exploit football to carve out a space for themselves," he said after the match. "They must be removed from society, identified, and the further away the better."
The Egyptian Football Association issued a statement expressing its "total condemnation of the vile racist incident" by some spectators who "went beyond the limits".
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