Armstrong has kept quiet since Usada's report was published earlier this month.
Asked whether Armstrong should confess, Wiggins told BBC Sport: "I think so yeah, yeah, definitely.
"But everyone knows he's a stubborn man. He has too much to lose, but the evidence speaks for itself. [It] looks overwhelming.
"There's a lot of anger. It's a shame cycling has being dragged through this again. It had to come out.
"Us riders here now - and I think I speak for all of us - we're the ones picking the pieces up and having to convince people the sport has changed.
"It's difficult to convince people because of the precedent that's been set and I haven't got the answer, other than to do what I'm doing."
Wiggins's fellow Briton Mark Cavendish described revelations about Armstrong as "frustrating", but insisted cycling is one of the cleanest sports.
"If you've done something, confess," he said. "That anyone can damage the sport I love right now, it's frustrating."
“It doesn't happen in other sports, not because they are clean, but because it's not got the structure cycling has”
Despite evidence of widespread systematic doping in the past, Cavendish maintains that cycling only appears to have more dopers because the testing is much more stringent than in other sports and insisted there are cheats in "every walk of life".
He told BBC Sport's Matt Slater: "There are cheats in entertainment, journalists cheat, every single sport has cheats.
"If you put the effort into catching them and you have a structure that does things properly, you're going to catch a cheat.
"It doesn't happen in other sports, not because they are clean, but because it's not got the structure cycling has. In my eyes, cycling is the cleanest sport."
"I've worked with David Millar," Cavendish said. "This guy's remorseful. He's repented."
He also praised others, including his former HTC-Highroad team manager Rolf Aldag, who admitted to doping during his time as a rider.
"These guys care about the sport," he said. "They ruin their reputation to move the sport on, but other people care more about themselves."
In his candid interview with BBC Sport, Cavendish also said he felt let down by Team Sky, arguing he was misled by the British-based team into believing they would compete for the green jersey - awarded to the rider with the most points, usually won by sprinters - in tours.
Matt SlaterBBC sports news reporter
"For Mark Cavendish, Team Sky is the long-distance relationship that has just not worked out. For Team Sky, Cavendish just does not work out for long distances."
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