"I joined [the police] as a very young person in Australia, I have worked on international investigations on organised crime particularly for the last 20 years, and I think this is eminently defeatable," Eaton told Reuters.
"I believe that by good due diligence, good regulation and good oversight, we will eradicate opportunities for criminality to take over this sport," added Eaton, who worked for Interpol for more than a decade before joining FIFA.
"We can defeat it, this is not an impossible situation at all."
The Turkish case resulted in last season's champions Fenerbahce being withdrawn from the Champions League while Serie A side Atalanta were deducted six points in Italy.
"This is an indicator of success, not an indicator of failure," said Eaton.
"The fact is, police are investigating when they weren't in the past, perhaps there's an interest in match-fixing when there wasn't before.
"This is not some sort of epidemic, this is an epidemic of enforcement, and this will help to break the back of criminal interest in football.
"It is a success story that these things are coming out, not a failure. It's dismaying for people to see but this means something is happening, it's not being ignored."
"It's good to see the national associations such as Korea working very closely with the police and very closely with the prosecutors, and making an institutional change to the way they pay players and regulate players," Eaton said.
"We're seeing the same approach in Finland, an excellent anti-corruption approach by the Finnish federation, in fact there is a strong universal collective effort to drive criminals out of the sport."
"We're trying to engage the referee, so far unsuccessfully, he retires this month but I'm endeavouring to speak to him and get his side of the story, it's not over."
