"2016 will go down as the year where the rules were changed," Brazile said of Trump's winning states — such as Wisconsin, Pennsylvania and Michigan — that usually go Democratic in presidential races.
"[Trump] ran a nontraditional campaign. I give him credit for that," Brazile said. "That said, you have to give credit to the campaign that had a consistent message 100 percent of the time — 'Make America great' ... a slogan that became the message that became the song. And you got a song, you got a melody."
"Donald Trump broke the blue wall. He cracked it, and then he broke it wide open, and then he siphoned off enough votes from disenchanted Democrats, independents and others that allowed him to win the electoral vote," Brazile said.
Gingrich said it's not a concern that Trump lost the popular vote, because the race is determined by electoral votes.
"The rules of the game as they were played meant that Donald Trump was president. When you're president, you're president. You have the mandate of being the president," Gingrich said.
"Whether he uses that mandate to unify the country and bring us together, which he should, is not a function of the size of the popular vote," Gingrich said. "It is a function of, 'What does a good president do?' A good president tries to represent all of America."
Brazile said she thinks Trump has an "enormous opportunity" to reach across the political divide after he takes office Jan. 20.
"He has an enormous opportunity, as every president in the first 100 days does, to show that he is eager to find common ground, to meet with Democrats," Brazile said.
"I mean, Chuck Schumer knows Donald Trump — both New Yorkers. Have him over for breakfast, have him over for afternoon tea and see if you can find common ground."
Gingrich and Brazile, who are longtime friends, reflected on how the country can heal after one of the most divisive elections in recent history.
"You know, it's a wait-and-see game," Brazile said. "There is so much that we can do together if we can find common ground."
Gingrich said, "My faith in Trump is I think he has the guts as well as the energy to have those kinds of meetings and to reach out to a broader range than maybe anybody since [Franklin Roosevelt]."