The four were members of the radical "Ultras Sur" group and the symbols displayed including a swastika and the German word "Totenkopf", a reference to the Nazis' SS paramilitary organisation, according to an official who asked not to be identified by name.
Real, who lost the match 1-0, did not immediately respond to a request for comment.
The fine of 3,000 euros for the four fans, who were not named and were also banned from sporting venues for six months, was the same as the sanction given to another spectator who shone a laser at Atletico coach Diego Simeone during the game, according to an Interior Ministry statement.
The punishments were imposed by Spain's commission against violence, racism, xenophobia and intolerance in sport.
(Reporting by Iain Rogers, editing by Ed Osmond)
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