The subject of doping has been brought into sharp focus recently, with the case of disgraced cyclist Lance Armstrong followed by revelations of widespread cheating in Australian sport.
Arsenal manager Arsene Wenger believes current controls in football are not strict enough to catch the cheats and WADA president Fahey agrees with the Frenchman, highlighting a need for increased testing for the blood-boosting drug EPO and the use of athlete biological passports in the sport.
"Whatever the sport, wherever it is in the world, more can be done," the Australian said at WADA's media symposium in London.
"I saw some examples recently, in tennis, where senior players were saying they were not tested terribly regularly. I would say tennis can do more, as can football do more.
"We're not in the business - and nor is any anti-doping agency - of reacting to rumour. You obviously have to be careful with the information you get.
"On the other hand, on a daily basis we get frequently anonymous information at our headquarters and we ensure the appropriate body is given that information to follow up.
"So we don't ignore it but one has to work on facts and it is not unusual for a losing team to blame something other than the ability of themselves for the reason for their defeat so you have to be a little bit careful and work on the facts.
"I simply say this about football - they are not testing enough for EPO. They can do more and we encourage them to do more.
"Again, use intelligence, not just more tests. While testing is a good deterrent factor and may be an effective way of catching people, I would argue the athlete biological passport is a very effective tool.
"Why isn't football using it? Again, why aren't the four football codes in my country using it? They can and in my view it would make them more effective.
"But I also recognise all of this costs money and I suspect some sports have got capacity to do it more easily than others and I can only encourage sports to see why this must be a priority to ensure the integrity of their game."
Sepp Blatter, the president of football's world governing body FIFA, tweeted: "Followed some key comments from @wada_ama media symposium today. Look forward to meeting WADA delegation in Zurich on Thursday."