The Romanians and Hungary, who beat the Faroe Islands 2-1, remain in contention to finish second in Group F behind Northern Ireland who defeated Greece 3-1 to reach the finals.
Romania are second on 17 points in Group F a point ahead of Hungary and three behind the Irish.
Hungary, who have a better head-to-head record, visit Greece while unbeaten Romania, who have conceded only two goals in the qualifying campaign, travel to the Faroes on Sunday.
"We’re disappointed because we failed to win but we must look on the bright side,” Hoban, who scored only Romania’s second goal in competitive matches in 2015, told reporters.
Romania's previous longest goalless run ended after 428 "dry" minutes in 1948.
“We still have chances to qualify," said Hoban. "If we beat the Faroes, we’ll qualify. If you do not beat the Faroes, it means that you don’t deserve to go to the Euros.”
Romania coach Iordanescu added: “We’re disappointed, we’re in a situation to depend on the last match. We played very good in the first half, we created many opportunities and we played offensively. It would have been completely unfair to lose this match.
“The goal put us in a tricky situation, we had to risk more to level the score. I apologise to our supporters.”
VOCIFEROUS FANS
The hosts dominated the match but wasted many chances, allowing Finland to break the deadlock on the break midway through the second half when Joel Pohjanpalo gave Ciprian Tatarusanu no chance with a precise shot.
Romania’s vociferous fans were frustrated with the team's failure to convert possession into goals once again with Dragos Grigore and Gabriel Torje hitting the post and Finland keeper Lukas Hradecky making a couple of excellent saves.
But Iordanescu’s men finally scored in the first minute of added time through Hoban, who finished from close range for his first international goal, ending Romania’s 429-minute drought.
Match organisers said the National Arena attendance record had been broken with 53,364 fans watching the game. The previous record was set in 2012 when 53,329 spectators watched Romania’s 4-1 loss to the Netherlands in a World Cup qualifier.
Romania were ordered to play against Finland behind closed doors following racist and violent behaviour by their supporters during goalless draws against Hungary and Greece.
But earlier this week, European soccer's governing body UEFA decided to further investigate the case and delayed punishment.
(Editing by Ed Osmond and Ken Ferris)
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