Coach Viorel Ion and assistants Marian Rosu and Romeo Bunica have been suspended from taking part in soccer-related activities for two years.
They were also fined 200,000 lei (£33,983) apiece, the FRF's disciplinary committee said in a statement.
Former striker Ion, who had a successful playing career at several Romanian clubs including Bucharest rivals Steaua and Rapid and German side VfL Bochum, said he would appeal.
"I will fight to the end and the truth will prevail," he wrote on Facebook on Thursday, denying any wrongdoing.
Fourteen Gloria players were suspended for between two and 12 months and fined between 10,000 and 50,000 lei.
Media reports of match-fixing and corruption have been rife in the Black Sea state for years with low-paid players being targeted in leagues across the country.
Marius Sumudica, coach of Romanian champions Astra, will serve a two-month ban at the start of next season for placing bets on domestic and international matches.
Betting on games is prohibited in Romania.
Last year midfielder Stefan Barboianu was sacked by Dinamo Bucharest over match-fixing suspicions.
(Reporting by Angel Krasimirov; Editing by Tony Jimenez)
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