Astro initially seemed reluctant to perform a survival song, telling the judges that he didn't see the point, although he changed his mind and performed an original rap after mentor LA Reid reminded him how far he had come.
Francis spoke to reporters after the show and said she was "very confused" by the teenager's attitude, according to The Hollywood Reporter.
"I think in that moment you should be pleading for your life and not throwing it away. I think Simon likes a little rebellion and he might respect Astro a little bit for being so rebellious," she said.
Francis added: "I don't understand his behaviour. I mean, he's 14, and you can call him a teenager and give him an excuse, but bad behaviour is bad behaviour. I think that he wasn't gracious in that moment. And I think in the whole scheme of things, no matter what you have to be grateful."
> X Factor USA result: Third Top 12 act eliminated
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Watch Astro's survival song below:
As for whether Astro's actions had made her own elimination harder to take, Francis said: "I think elimination is elimination. It would've been hard either way.
"The thing you get disappointed about when you see someone like Astro have such an obnoxious attitude is that he gets to stay. That's kind of a hard pill to swallow, because he doesn't seem grateful to be here."
Francis, who had been mentored by Nicole Scherzinger, had previously told fans on Twitter that she didn't think her Rock Week performance of 'It's All Coming Back To Me Now' had been one of her best.
"I came home and watched my performance last night. It was not great. I was off key. I couldn't hear the music but I didn't know it was so off till I watched it back...," she wrote. "I can be honest about myself. I was too nervous. And I couldn't hear that combination got me in trouble."
> X Factor USA Rock Week results show, Rihanna performs - pictures
> Read Digital Spy's full X Factor headlines
Francis also took to her Twitter account following the results show to admit that she was "heartbroken" to be leaving the competition, but told fans she was looking forward to returning to her family.
She has also said that she hopes to be managed by Irving Azoff of Front Line Management Group going forward.
Astro, meanwhile, posted a series of tweets on his own account following Thursday's live show, saying: "Politics!! don't be fooled by what you don't know! Thank you AstroNauts for holding me down!
"Its funny how people are quick to judge not knowing whats going on behind the scenes. Maybe I should have given my Disney smile instead!"
He added: "I wasn't talking about viewers when I said I don't wanna perform. If you only knew what I know you'd say otherwise. Time to relax and reflect. Deuces!"
X Factor's remaining contestants are Astro, Josh Krajcik, Lakoda Rayne, LeRoy Bell, Rachel Crow, Drew, Marcus Canty, Chris Rene and Melanie Amaro.
X Factor continues on Tuesday at 8/7c on Fox
Watch Stacy Francis's survival song performance below:
Browse a gallery of pictures from the results show below: