Couric, who received Cronkite's blessing for her leadership over the broadcast he once led, said she received ongoing support and guidance from the media legend who died Friday at age 92.
But why is Couric daunted?
Couric said she's lately been reminded of the great newsman's work, saying that he was "unbelievably committed to his craft."
But Couric said Cronkite once told her at a dinner party he had confidence in her.
Couric said at the party Cronkite shared his thoughts on the intense scrutiny of the lead anchor position at CBS News. Like Couric, Cronkite also faced heavy criticism for his reporting.
Couric, who has held the lead anchor position at "CBS Evening News" for three years, said, "...He got grief from both sides of the aisle, as have I...It made me feel much better about some of the criticism you often take when you're in this position."
The media world owes Cronkite a "debt of gratitude," Couric said, for his contributions.
"When television was in its infancy, he really shaped the medium in a way that I think no one else could have," Couric said. "...He emphasized accuracy, fairness, objectivity, decency, humanity and getting to the story and making the news more important than the person delivering it."
Over dinner, Couric and Cronkite also swapped stories. Cronkite shared his experience of covering the Nuremberg trials, and Couric said she told stories about her father who was a United Press journalist, like Cronkite.
Surprisingly, Couric said, they also talked about the talent competition, "American Idol."
"He was just an extraordinary person first, I think," Couric said. "And an extraordinary journalist second."