The 28-25 defeat means England will likely have to beat Australia next Saturday to avoid the humiliation of being the first host nation not to make it into the knockout stages.
"I am very convinced (we will still qualify). Because of all the hard work we've done over the last 12 or 13 weeks, because we're a tight-knit group. It's a challenge we accept and one we are all looking forward to," he said at a news conference on Sunday.
"There's nothing better than when you lose a game, how upset and annoyed you are about it. At least we can focus our minds straight into another game.
"If the season had ended now it would drag out that much longer. The best thing after a defeat is having a game after it. Now we can really focus our minds on this weekend."
In the dying minutes of the match, England captain Chris Robshaw spurned the chance to take a tricky kick at goal that would have evened up the scores.
It was a decision that could haunt him for the rest of his career if they don't qualify.
Asked whether the team need to support Robshaw after his decision to go for a lineout which failed to result in a match-winning try, Youngs said: "It's not about rallying around Chris, it's about rallying round each other."
"We back it all, back the group, back the decision. We went for the win. I don't think the game came down to that one moment. It came down to moments before that, 20, 30 minutes before that, when we were giving away penalties and letting them back into the game.
"Ill-discipline from us let them back in the game and it was a real shame."
A battered and bruised Wales were second-best for most of the match before Gareth Davies collected a chip kick to score a try and a seventh penalty from flyhalf Dan Biggar clinched a famous victory.
"It was a great effort...They got on the outside of us and kicked the ball inside and it was a fairly good pick up to score. It was one of those moments you can't quite believe it's actually happened," Youngs said.
(Reporting by John Geddie)
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