The Benetton wing cites last year's win against Australia as a breakthrough moment for Gli Azzurri in terms of their status in the sport.
Lynagh – the son of an Italian mother and former Australian rugby player Michael Lynagh – told Rugby World magazine: "Italian teams in the past have maybe lacked that confidence to finish the job.
"But with this coaching team, and especially with the players, the young talent we've got, we don't want to be treated as whipping boys anymore. We've got serious talent now and we're adding detail to that talent.
"We saw gaps in Australia's game that we thought we could go after. Everyone in the team and in that game played incredibly well. We scored tries, they came back, but ultimately we pushed through and showed we had that killer instinct."
Lynagh admits that he found it "weird" rooting against Australia, particularly with his younger brother Tom Lynagh representing the Wallabies.
He said: "It was a bit weird for me. I grew up supporting Australian teams in sports, along with Italian teams. So playing against these guys who my brother knows really well, and I know really well too, was strange. But after a few minutes, it's just another game and you treat it that way.
"We've got Australia next summer in Perth (in the Nations Championship) so I really hope I get the chance to play against Tom as well. That would be pretty cool."
Lynagh thinks that the win against Australia proves that Italy are capable of competing with the powerhouses of international rugby.
The former Harlequins player said: "We're not only staying in games against these major opponents, we're looking like we can win and then actually winning them.
"I feel that Australia game was a huge, huge momentum shift from getting one-off victories against Wales or Scotland in the Six Nations to saying, 'Right, we are one of the best teams in the world. Let's believe in ourselves and play in a way that reflects that.'"