Mr Zentai is accused of murdering an 18-year-old Jewish man in November 1944 while serving in the Hungarian army. He refutes the accusation as well as further accusations he beat the man to death and threw his body into the Danube River.
The Federal Court ruled Mr Zentai could not be extradited for the reason that the specific offence of "war crimes" did not exist in Hungarian law in 1944.
The commonwealth maintained that while the specific offence did not exist in 1944, the alleged acts could be charged as murder, which was a crime in ‘44.
It was not until 1945 that Hungary passed laws concerning war crimes.
Israel director Efraim Zuroff held the position that suspect offenders had been extradited from other countries to stand trial in Germany over war crimes that had not been recognized as such when they were allegedly committed.
"(This) signals a dismal conclusion to Australia’s totally unsuccessful efforts to bring to justice any of the numerous Nazi war criminals who found refuge in the country," Dr Zuroff said in a statement.
The Nazi-hunting Simon Wiesenthal Centre has slammed the Australian High Court for refusing to extradite Mr Zentai. They have long argued that the alleged murderer should face a Budapest court.
"Today is a sad day for Australia and for justice, but most of all for the Nazis’ victims, their families and those who empathise with their suffering," he wrote.
Accused Charles Zentai is age 90 and was purportedly one of three Nazi-backed Hungarian soldiers who tortured and killed in Budapest.