Victory over Belgium would have secured Spain second place behind already-qualified Georgia in the Rugby Europe Championship standings and a ticket to next year's World Cup in Japan.
The shock defeat left Romania to progress and the Spanish now face an arduous series of playoff games if they are to get through to the game's showpiece tournament for the first time since 1999.
Spain were overwhelming favourites to beat Belgium but rarely got going on a mud-caked pitch in Brussels and ugly confrontations broke out at the final whistle as members of the Spanish coaching staff tried to restrain their players.
Referee Iordachescu was pursued by furious Spain players and several irate supporters and needed to be escorted off the pitch by competition officials.
Spain's rugby federation said it had warned the referee commission of governing body Rugby Europe about appointing Iordachescu to the game.
"Romania needed Spain to lose in order to go to the World Cup, evidently, a Romanian referee was not ideal for this game," said a statement on the organisation's website.
"The federation will present a complaint to Rugby Europe, copying World Rugby, so that the Commission of Referees can review the video of the game and determine if the referee deliberately favoured Romania's interests and, if that is the case, take action."
The statement also condemned the reaction of "some of the players who could not contain their feelings" after the defeat.
Rugby Europe responded by saying the appointment of Iordachescu was made independently.
"Rugby Europe has always operated the highest standards of match official selection whatever the competitions," said a statement on the organising body's official website.
"As for other international major competitions, referees’ appointments for Rugby Europe Championship have been made ahead of the competition by an independent and neutral skilled committee.
"It has been reviewed and confirmed during the tournament based on referees’ performance at international level.
"While we appreciate that this is a subject of high-emotion, it would be inappropriate to comment on match official performance before the usual full review has been undertaken."
Spain will now need to beat Portugal in a playoff and then win a two-legged tie against Samoa in order to reach the World Cup.
If they beat Portugal but lose to Samoa they will play in a four-team repechage in November in a last attempt to qualify for the competition.
Spain coach Santiago Santos also criticised Iordachescu in his post-game news conference.
"We weren't allowed to play, the referee kept stopping the game at every moment," he said.
"The difference between penalties against us and for us was huge. When we were trying to come back in the game the play kept on being interrupted. I said to one of the players that Spain didn't lose today, rugby lost."