Football match-fixing brought "huge fraudulent winnings" against legal and illegal gambling institutions, Eaton added, although he did not have any figures on how much gambling on football is worth specifically.
FIFA president Sepp Blatter last week pledged 20 million euros for a dedicated anti-corruption unit based in Singapore to fight match-fixing, which police officials said was a low-risk, high profit form of crime.
"Criminality involved in fixing football matches is global, enormous and organised," Eaton said. "Football is too respected globally to not be protected."
"These are criminals taking advantage. They are not to be respected, they are not Robin Hoods, they are not good people. They hurt players and they destroy careers."
The unit, in a partnership with Interpol, aims to develop a programme for football officials, players and administrators that warns against match-fixing and alerts them to how it dishonours the game and might ruin their careers.
It will involve international education and training over e-learning. Interpol will also brief and debrief players before and after every competition to ensure they are fully aware of what match-fixing might do to their careers.
"We protect young players, we protect young referees by teaching them to resist the temptations that these people are trying to take advantage of," Eaton, a one-time Interpol officer, said.
But the unit will not actively seek to clamp down or prosecute match-fixers.
"FIFA is a football management organisation. It is not an investigation organisation. We don't conduct a lot of security operations with a little bit of football. We conduct a lot of football with a little bit of security," Eaton said.
"Prosecution is not my priority, in fact, not a priority at all."
ANTI-CORRUPTION REPUTATION
The anti-corruption education wing will be based in Singapore due to its low tolerance for corruption, and Eaton believes the Football Association of Singapore (FAS) has a model that is one of the most committed to anti-corruption in the world.
"Asia is a hotbed of betting and match-fixing and Singapore is among the least corrupt countries on the planet so there may be no better place to set up this initiative than in Singapore," Interpol secretary-general Ronald Noble told a Zurich conference last week.
However, some people might have slipped through the cracks.
Eaton recently said in an interview that an "academy of match-fixers" run out of the wealthy city-state might be responsible for rigging matches around the world.
A Singaporean man has been arrested in Finland on such allegations.
Eaton was with Interpol for more than a decade, and was manager of operations before joining FIFA in April last year.
Bringing with him an extensive police background that has allowed FIFA to tap into Interpol information more readily than it could before his app
