The actress became the second star to be fired from the NBC competition on Sunday night after serving as project manager for the women's team, who lost the challenge.
"I thought I was a really tough chick and could handle it," she told Ryan Seacrest on his KIIS-FM radio show. "I went in there feeling good and positive and playing for my charity.
"I have a business and do many things, I have people that work for me, and was thinking I can do it, but they had some alliances and they went after me. I feel like I did the best I could. There was nothing I could do. I was dodging knives and bullets!"
The star, who further described her early firing as "humiliating", went on to tell Seacrest that she knew she would be going home if the women lost as soon as they encouraged her to take on PM duties, yet added that she was happy to return to her kids.
This week's challenge involved writing, creating and performing a children's book for an audience of 4 and 5 year olds. The women's idea involved a lion who didn't know how to roar, but they eventually lost the task on originality and creativity points.
Rinna later thanked her fans for their support on Twitter, writing: "Have I told you lately that I love you?! This girl feels your love and I thank you all!! #LOVE (sic)"
Celebrity Apprentice airs Sundays on NBC.