Jerome Valcke, alongside UEFA general secretary Gianni Infantino and Interpol counterpart Ronald Noble, was speaking at a match-fixing conference in Rome attended by other soccer and police representatives as well as gambling experts.
"I am sure that at the level of the Champions League and the World Cup that there is no match-fixing," Valcke said, adding there were too many systems in place for problems not to be spotted.
"What we have to look at are the lower leagues and where they're just starting to play football."
In contrast to Valcke's view, media reports and several books have questioned the results of certain matches at the very top level of the game but qualifiers for big international tournaments are where problems certainly lie.
In August, Malta midfielder Kevin Sammut was given a 10-year suspension by UEFA after being found guilty of match-fixing in the Euro 2008 qualifier between Norway and Malta.
The same month, European football's governing body also launched a match-fixing probe over a Europa League qualifier.
"We need Europe to understand that we must have a common legislation on match manipulation," Frenchman Valcke added.
"As long as there isn't common legislation in Europe, and along as you don't have the same sanctions in every European country, it's easy (for the fixers).
"As long as there isn't an understanding from all parties that law enforcement, national and European authorities and the football family are all working together there is no chance we will succeed."
UEFA's Infantino also sounded the alarm.
"We are not geared up to fight criminality. We are geared up to deal with fouls from behind or maybe some stadium violence," he said.
"It's not like doping, where we can make tests and we know whether something is dope or not."
Italy, the venue for the conference, has long battled a match-fixing problem in the top flight but progress has been made in catching wrongdoers.
Interpol set up a specialist match-fixing task force in 2011 which helped Italian authorities with the investigations that led to the arrests and bans in the 'calcioscommesse' betting and fixing scandal, in which gangs from Asia were implicated.
The same year world soccer body FIFA donated 20 million euro ($26.59 million)to Interpol, the largest sum the international police body has ever received, and announced a 10-year partnership to help take on the fixers.
The fixing of sporting events has come to be dominated by criminal organisations from the Far East.
The sport gambling markets in Asia are said to be worth hundreds of billions of dollars a year and the gangs' power to arrange results and manipulate matches has hurt the credibility of some sports on their continent.
Forty one South Korean players were handed worldwide lifetime bans by FIFA this month following a match-fixing scandal in the country's K-League.
The Asian gangs have now infiltrated Europe and the Americas too with Interpol's Noble describing the networks as "a many headed dragon that we must slay".
Noble warned against complacency from football authorities, particularly those from countries where match-fixing is believed to be non-existent.
"A German court recently found that a European-based syndicate fixed a match in the Canadian league," American Noble said.
"Based on interviews with players and officials, a recent article in Canada revealed that players in this obscure league were regularly approached to fix matches, and the journalist reporting on this issue has received death threats following that.
"The Canadian match fixing scandal demonstrates the long reach of match fixers in all types of leagues all around the world, and also that it's necessary for the law to have an equally long reach.
"Canada is but one of many countries which has uncovered match fixing in its football leagues... No country is immune - none."
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