The Argentine was sanctioned with four games for slapping the fourth official on the back of the head after his first-half dismissal on Friday, two for protesting, one for applauding the decision and another for giving instructions to the team from the stands.
Diego Simeone was sent off for "protesting openly with his arms in the air, going out of the technical area on repeated occasions and not listening to the fourth official who warned him to stop," RFEF said in a statement.
It added that Simeone then "hit the the fourth official on the head with his open hand twice" and "applauded on several occasions in a sign of disagreement" with the decision before going off.
Finally, "he took no notice of instructions" to move away from his position in the stand.
The incident took place in the first half of the fiery clash with Real at the Calderon which Atletico won 1-0, and 2-1 on aggregate.
Simeone accepted afterwards that he was wrong but Atletico are likely to appeal against the severity of the decision.
"The people that decide will have to give the sanction that they think is right. When someone does something wrong they need to pay for it and we are waiting to hear what we have to pay," Simeone had told a news conference on Sunday.
La Liga champions Atletico starts the defence of their title on Monday against Rayo Vallecano and Simeone will be absent from the touchline for that game due to a ban carried over from the last campaign.