The club were responding to a piece on the RFEF website saying Real's game at Atletico on Thursday would be "under the close scrutiny of Mourinho, who feels he has been mistreated by officials in recent league matches."
Real issued an official statement to express their "indignation" at the wording, which was not the same in the latest version of the article on Wednesday.
"We consider it enormously serious that these remarks about our coach were made on the Federation's own website," Real said.
"They clearly demonstrate a prejudice that is a long way from the objectivity, neutrality and balance which should inform the organisation's official publications.
"We demand action is taken for what we believe is a lack of respect and consideration to the coach of our team, the club itself and the fans."
Real won the first leg of the King's Cup quarter-final tie against Atletico 3-1.
CALM SITUATION
The RFEF moved quickly to calm the situation, with a spokesman telling Spanish radio the article had been written by an intern and in no way represented the federation's opinion.
"We should not be making value judgments in the federation, but on our website there are interns who write," spokesman Jorge Carretero said.
"As soon as we saw it we took it down," he added. "It's absolutely not from the federation."
Mourinho, renowned as an outspoken figure, was banned for two matches this season for verbally abusing a referee.
At a news conference on Wednesday, the Portuguese repeated his view that Real had been denied what he felt were two clear penalties in Sunday's 1-1 draw at Almeria which left his side four points adrift of La Liga leaders Barcelona.
"I do not doubt the honesty of referees but there are some things that are obvious and that people who are not hypocrites have no problem in admitting," Mourinho said.
"There were decisive penalties in the match that weren't given and this is not a criticism but something obvious."
