"His biggest mistake was just being Geraldo," Gibbons joked.
Rivera explained that he had been fighting an uphill battle the whole way.
"I was butting heads with my team from day one," Rivera said. "Kevin Jonas, Ian Ziering and Lorenzo Llamas -- they wanted to kill me from the first minute they met me. I had a big bull's eye on my back, so I was punching my way through it."
Another person fighting a tough battle is fellow newsman Brian Williams, who has been suspended from NBC Nightly News for six months without pay after admitting to making a false report in 2003. Williams incorrectly stated that his helicopter was shot down in Iraq.
Rivera passionately defended Williams, claiming that NBC's punishment was inappropriate.
"I think NBC imposed the Draconian death penalty on Brian Williams, and I think it was totally out of line. It was excessive," Rivera said. "They wrecked his career for a single mistake."
With her victory, Gibbons joins a list of Celebrity Apprentice winners that includes Arsenio Hall, John Rich, Bret Michaels and the late Joan Rivers. She and Rivers are the only female winners from the celebrity edition. During the finale, the show paid tribute to Rivers and her daughter Melissa made an appearance on the show.
"Melissa came into my dressing room prior to that live shot and poured her heart out about what things were like," Rivera said. "It was painful, but she really has pulled it all together and is making a real effort to carry on."
This week, Melissa -- a former ET intern -- will conduct a series of special interviews, including a sit down with Academy Awards host Neil Patrick Harris, which will air Thursday, Feb. 19.