After being stripped of his seven Tour de France titles by the International Cycling Union (UCI), the IOC opened an investigation into the Armstrong doping scandal last week which could ultimately see Armstrong (pictured top) lose the time trial bronze medal he won at the Sydney 2000 Olympics.
Although the IOC has an eight-year statute of limitation for changing Olympic results and stripping medals from doping offenders, which has now expired in Armstrong's case, it could get around this as the statute was interrupted through the American lying about doping.
If Armstrong is stripped of his Olympic bronze medal, it could be reallocated to Spain's Abraham Olano, who finished fourth in the Sydney 2000 time trial race.
But Fasel feels the issue is almost irrelevant now.
"Regardless of whether you take his Olympic medal, his credibility is lost," Fasel told insidethegames.
"This is almost administration at this point and the taste will remain bitter whatever happens.
"The most important thing is looking at what we can do to avoid this happening again in future.
"I am against witch-hunting.
"We should not need to witch-hunt with athletes when it comes to doping but rather educate them and their coaches and their entourages about the importance of not doping.
"Education for me is much more valuable than anything else.
"But with this Armstrong issue, more than anything else I feel very, very sad.
"You have this great star and role model and then you find this.
"It is not a huge feeling of victory for me but just very sad.
"I only hope it will be a lesson to athletes that if they cheat, a day will eventually come where they will be caught.
"But it is very concerning not only to the IOC but for every sports federation because doping is a huge threat to the integrity of sport.
"You cannot expect fans to trust you and believe in you if you are cheating."
Fasel, who is also President of the International Ice-Hockey Federation (IIHF) and the Association of International Olympic Winter Sports Federations (AIOWF), admits he has some sympathy for under-fire UCI President Pat McQuaid but that the problem of doping in cycling needs to be looked at urgently.
"For sure it is not an easy situation for him [McQuaid] and he is exposed because his sport is one where doping has been a big problem for a long time," Fasel explained.
"The question for me is what can we do to help the sport?
"Some people say we should kick cycling off the Olympic programme or that we should take cycling out of all elite major sports events.
"I don't have the answer on that here but we have to do something for sure.
"Even if you take the Tour de France, is it right that the athletes have to go twice on the same day up the Alpe d'Huez?
"This is a huge question mark for me.
"Maybe it is good for the fans but if you put athletes in a situation where they have no choice but to take illegal substances just to compete, that is wrong.
"There must be dialogue with the athletes so they are not pushed to that situation.
"It is the same with my sport of ice hockey, looking at protecting the athletes by not pushing them too hard.
"I am against having the Roman gladiator for an athlete because we are not at that point anymore.
"Sport must be a great show and it must be entertaining but not at all costs to the athlete.
"First and foremost, it must be safe and it must be clean."
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November 2012: IOC to investigate Armstrong doping scandal
August 2012: Exclusive - Armstrong set to be allowed to keep Sydney 2000 Olympic medal despite drug ban