FIFA suspended Balogun's red-card ban and cleared him to play in the round-of-16 tie after US President Donald Trump personally urged FIFA President Gianni Infantino to review the case.
The RBFA said it had had "only a few hours" to act, while no information was provided by FIFA.
"For an appeal to be admissible, FIFA's own regulations state that the reasoned decision must first have been communicated to the appellant," the RBFA said in a statement.
"While the RBFA was merely seeking legitimate explanations, FIFA itself created an appeal and immediately ensured that it would be declared inadmissible.
"All of this occurred while FIFA simultaneously refused to respond to the RBFA's legitimate requests."
The RBFA said it was challenging Balogun's eligibility after FIFA removed the automatic player suspension section from a pre-match coordination meeting presentation and failed to explain the change despite repeated oral and written requests.
Reuters has contacted FIFA for comment.