The federation was asked to take appropriate disciplinary measures against the pair by a Spanish government commission that seeks to combat violence and intolerance in sport.
The commission argued their row, which boiled up after Preciado was incensed by Mourinho's suggestion that his team had not made a serious attempt to beat Barcelona earlier in the season, had risked creating a hostile atmosphere around Real's La Liga match at Gijon.
Gijon said on their website on Wednesday the RFEF's competition committee had decided the coaches' statements did not merit punishment.
The committee had, however, urged all those involved in football to "moderate their statements", the club added.
Preciado accused Mourinho of lacking respect and made disparaging remarks about the Portuguese at a news conference, prompting Real to release a statement before the match condemning his comments.
Several La Liga coaches, including Villarreal's Juan Carlos Garrido and Espanyol's Mauricio Pochettino, backed Preciado.
