The controversy erupted when video footage emerged - and was circulated widely by "Fernando Alonso's management" according to Sport Bild - of Sebastian Vettel purportedly overtaking illegally under yellow flag conditions at Interlagos.
Ferrari confirmed that it asked the governing body for "clarification", and spokesman Luca Colajanni insists the Maranello team has "until tomorrow (Friday) to file an appeal".
British newspapers quote F1 chief executive Ecclestone as blasting the affair "a complete joke".
"It was a super race, a super championship. Now everyone is talking about this," he said.
Ecclestone said the subsequent furore is a "joke" because of the "fact" that Vettel overtook only once he had passed a waving green flag.
"I don't think there needs to be any action taken. It's completely and utterly wrong," he added.
"It's a very silly, bad thing for anyone to do to push this because there is nothing in it. Ferrari had a great season but this was a mistake."
And he told Germany's Der Spiegel: "Vettel will suffer no consequence and will remain the 2012 world champion."
Indeed, FIA spokesman Norman Howell indicated that the Paris federation will now spell out the news to Ferrari in a formal letter of response.
"Now that Ferrari has sent us a letter asking for an explanation we will give it to them," he said.
F1 race director Charlie Whiting added: "We never had any doubt that Vettel's overtaking was compliant.
"There were conflicting flags and lights," he acknowledged to Germany's Sport Bild. "It was investigated during the race, with the result that there should be no punishment."
An FIA spokesman added: "Vettel's title is not in danger. A further investigation will not happen."
However, Ecclestone acknowledged that another route open to Ferrari is civil action.
"But the case is flawed before it starts," he told the Telegraph. "Nothing is going to happen."
But what has happened already is the criticism of Ferrari and Spaniard Alonso. Germany's Berliner Kurier accused them of being "sore losers".
And the Bild-Zeitung daily said the efforts to have Vettel's championship overturned are "Unfair. Un-ferrari".