The punishment followed anti-Semitic chanting by fans in a friendly at home against Israel in August, for which the Hungarian FA (MLSZ) expressed regret, but it was unhappy with the ruling to play the 2014 World Cup Group D qualifier behind closed doors.
"That the Hungarian national team must serve its punishment at a vital game in the most prestigious international tournament for an incident at a friendly game seems overly harsh and unfair even before receiving the precise reasoning," the MLSZ said.
"Therefore MLSZ will file its appeal after it receives the ruling in order for a more just decision in proportion to what happened (in August)."
The MLSZ added it wrote a letter after the August friendly to the Israeli ambassador in Hungary and the Israeli Football Association and FIFA to apologise, in which it "condemned the actions of a minority of fans at the game."
"Considering the extremists behaviour experienced at the game, FIFA's actions against such incidents is understandable," the MLSZ added in the statement released on Tuesday, having cancelled a previously scheduled interview with Reuters.
"MLSZ - like FIFA and UEFA - is still determined to expel from the stadiums hateful acts and fan behaviour that do not adhere to the spirit of fair play.
"It is committed to making sure extremist voices that do not adhere to civilised norms disappear from Hungarian football fields as soon as possible."
On top of the anti-Semitic chanting last August, Hungarian fans also waved Iranian flags at the Israeli team, who were warned of a "severe threat" to their safety.
Hungary and Romania, who meet on March 22, are locked on nine points from four games, three behind group leaders Netherlands and six ahead of any challengers for second spot.
Given the importance of the game there were contrasting reactions in Budapest and Bucharest.
Hungary's national sports daily ran a full front-page image on Wednesday saying "Locked out!" and called the decision "shocking" while fan pages on social media sites exploded with condemnations of FIFA and its leaders, often repeating anti-Semitic slurs.
Romania's sports press was jubilant over the ban on spectators, believing it will help their team in its efforts to qualify for their first World Cup since 1998. Hungary have not made it since 1986.
In an article headlined "We've escaped from the inferno of Budapest", Prosport quoted former player and coach Emerich Jenei as saying: "It's a huge advantage. I know the Hungarian public well and know what I'm talking about."