Clinton also gave her opinion on President Trump's United Nations address earlier Tuesday in NY, where he incredulously referred to North Korean leader Kim Jong Un as "Rocket Man" and threatened to "totally destroy" North Korea in the event of nuclear threat against the U.S.
But she warned that Russian Federation would continue to try to influence American democracy.
Clinton said Tuesday night that Putin interfered in the presidential election in part because of her work as secretary of state, which brought the two into conflict on various occasions.
"You are both required to stand up for the values of what we believe in - democracy and opportunity - as a way to demonstrate clearly the United States remains the beacon that we we want it to be, while of course, when you face risky situations like what is happening in North Korea, to make it clear your first approach should always be diplomatic", she told Colbert.
"I think no one, including me, is saying we will contest the election", Clinton clarified speaking at a Mic roundtable in NY on Tuesday. "Not the kind of message the leader of the greatest nation in the world should be delivering", said Clinton.
During a publicity stop to promote Clinton's new book, What Happened, bookstore owner Lissa Muscatine told a crowd that Clinton and her husband, former President Bill Clinton, bought pizzas from Comet Ping Pong and sent them to a local after-school literacy program.
Clinton - who recently embarked on what critics have called a "blame game" book tour for "What Happened", her account of her loss to Trump last November - claimed her gender bothered Putin and made him "agitated".
"I think depending upon what is found in those investigations, it won't be just me, it will be millions of Americans who raise questions about the legitimacy of the election", Clinton added.
Clinton said the "approach should always be diplomatic".
"I don't think anybody can with a straight face say that the Russians did not set out to influence our election, and they did so", Clinton said.
"And not call him Rocket Man", she continued.
But Putin was not Clinton's only target during the interview.