Armstrong won seven straight Tour de France titles from 1999 but had them stripped when he was found guilty of doping in October last year before he spoke about his wrongdoings for the first time on American television last week.
Wiggins at first said he would not watch the interview but the Briton in the end tuned in - with his seven-year-old son for company.
"It's heart breaking for the sport and then the anger kicks in. It was difficult," Wiggins told reporters on Thursday at Team Sky's training camp in Mallorca ahead of his season opener on the Spanish island.
"By the end of the hour and a half, I had the best feeling in the world. Part of me didn't want to watch it. The fan in me didn't want that perception of him as an amazing athlete to be broken.
"Then I got quite: 'You deserve everything you got.' So within two hours of watching the whole thing, the emotions were up and down. By the end I didn't feel any sympathy for him at all."
Wiggins, beaten to third place by Armstrong in the 2009 Tour, said he had felt enormous pride when he told his son he was no cheat.
"I had to explain it to my son because he'd won the same race his dad had won," said the 32-year-old father-of-two.
"When he (Armstrong) started welling up about his 13-year-old son, and him asking what's all this about. I never have to have that conversation with my own son as his father's won the Tour clean.
"There's this element of being quite smug about the whole thing. Watching him suddenly cave in after all these years of lying so convincingly, there was a lot of anger, a lot of sadness and I was slightly emotional as well, if I'm honest.
"It was difficult to watch. My wife couldn't watch it and walked out of the room."
- Sports & Recreation