A report released earlier this week by European enforcement agency Europol said 380 matches were under investigation, including one 2009 Champions League game in England between Liverpool and Hungarian club Debrecen.
While there has never been any suspicion of wrongdoing by anyone at Liverpool, who won the match in question 1-0, Arsenal manager Arsene Wenger this week claimed the whole situation must act as a wake-up call to the English game.
Eaton - a former manager of operations at Interpol who left his post at FIFA in March 2012 and is now director of sport integrity at the International Centre for Sports Security in Qatar - maintains everyone must be guarded to ensure the on-going integrity of what is the world's most watched football competition and biggest gambling market.
Eaton told BBC Radio Five Live's Sportsweek programme: "You hear a lot of allegations, but I have never had any credible evidence about fixing in the English Premier League or the Champions League - that does not mean you should not be vigilant.
"You must be vigilant, this is the most watched league in the world, the most gambled league in the world and therefore the one who has to be the most vigilant."
Eaton revealed there are many different ways matches could be rigged, with the "five star fixes" those involving players from both teams as well as officials.
"There is no standard form, with a lot of different styles engaged by match-fixers over the years, including ghost games which did not exist in reality, but were called by the monitoring agencies," he said.
"There was the fake Togo team in Africa. Mostly it is about compromising players or officials, referees," he said.
"Organised crime take an interest in this, which is not because of the growth of match-fixing, but because of the great growth of gambling in south-east Asia, particularly on European football, we also saw this with the Mafia being involved in match-fixing in Italy. The betting fraud is the main purpose."
Eaton believes strict regulation on a global scale will help clamp down on those looking to rake in lucrative profits from rigging games.
He added: "You are well regulated in the betting environment in the UK, but it is not very well regulated in south-east Asia, it is 'grey gambling'. It dwarfs the European market significantly, it is probably up to 100 times bigger, which makes it such a huge attraction for organised crime.
"Historically match-fixing was all about positions on a league ladder, avoiding relegation, perhaps even some casual spot fixing among colleagues as well, but these are inconsequential compared to what is happening today in terms of organised crime using it for betting fraud, which is all about timing and making sure the bookmaker is not alerted early, trying to put a plunge very late in a match.
"What has to happen is the governments of the world need to get together and regulate betting internationally.
"It is no longer suitable for gambling to be regulated at a national level."
Stoke chairman Peter Coates, who helped found bet365 in 2000, echoed the support for tighter international regulation.
"We should be constantly vigilant, that is clear," he said.
"The UK is very clean, I am not saying nothing ever goes on, but it is up to us to make sure it does not and to play our part," he said.
"This is going on out in places where it is unregulated, like the Wild West, and these are the problems."
Coates added: "What there is is a case for is regulation, we have the best (betting) regulation in the world here in the UK and the more people who copy it, the better we will be.
"We have a Gambling Act in this country and if we see anything suspicious, we have to report it. If we did not, then we could lose our licence and the business would be gone."