Clinton's lead over Trump in the national popular currently exceeds 2.4 million votes, according to the Associated Press.
When asked by ABC's George Stephanopoulos if it is appropriate for Trump to make false statements like that, she said, "Many people are questioning the victory. You got people spending millions of dollars, wasting money and time in the Clinton and [Jill] Stein camp in Wisconsin, Michigan, tried in Pennsylvania to recount. So not everybody has ... accepted the election results."
"But to your question," Conway continued, "the president-elect has been talking to different people including Kris Kobach, [secretary of state] of Kansas, about voting irregularities or the number of illegal votes that may have been cast, and I believe that he bases his information on that."
Asked again by Stephanopoulos if the statement by Trump is true, Conway responded, "Well, he's been receiving information about the irregularities and about the illegal votes, particularly from sources, officials like Kris Kobach as I mentioned, but he is messaging to his supporters and to the rest of the country the way he feels."
Conway said Trump won because he had a message that connects with Americans. Addressing the Americans who did not vote for Trump, Conway said that they now "can't get past the grief, denial and anger stages and into the acceptance stages," which she said "really defies what Secretary Clinton and President Obama themselves had said" about coming together as a nation.
Though Clinton won the popular vote, Conway said Trump will still reach those Americans who did not vote for him, because he will "be the president of all Americans, including those that did not vote for him."
Conway was also asked about Trump's rally in Cincinnati, Ohio, Thursday night, where some Trump supporters chanted in reference to Clinton, "Lock her up."
"That's the way they feel," Conway said, "And there would be officials who are in charge of such things in the Trump administration who may look at that again. But Donald Trump made very clear last week as the president-elect that he's moved on from that. That he's focused on ... more focused on things, like health care, immigration, bringing jobs back."
When Conway was pressed on whether the Trump administration may pursue prosecution against Clinton, Conway replied, "No, I'm not suggesting that at all. That would be something I would not be able to say."
"But reminding everybody what the president-elect said last week," she continued, "He's moving on to focus on the future, not the past and he has said to The New York Times on the record he thinks that the Clintons have suffered enough. Of course, the Department of Justice, the different committees, the FBI perhaps can take a different look, but nobody expects and nobody is talking about that right now."
ABC News' Corinne Cathcart contributed to this report.