The singer left the competition on Sunday after the judging panel voted to save Hannah Barrett following a tense 'sing-off' during the live results show.
Girls category mentor Nicole Scherzinger abstained from choosing between her two acts, but Gary Barlow and Sharon Osbourne voted for Hannah to remain in the competition, while Louis Walsh said he would have also saved Hannah despite not needing to vote.
Speaking about her elimination, Abi said: "I was sad that I felt there was an air of disappointment surrounding me.
"But the process is incredibly stressful and I feel like my nerves and my lack of confidence let me down when I went out there on a Saturday night."
"When it comes to the sing off, that emotion that you feel, you can't replicate that when you go out on a Saturday night. As much as you might try, you can't mimic that vulnerability you feel, and that sort of 'Oh my gosh, this could be the last time'."
Abi left the competition following a 'Big Band' themed show on Saturday.
She said: "As much as the themes probably weren't my cup of tea, I absolutely loved big band week. I loved being on the stage with all those musicians."
The former supermarket worker has also thanked her fans for their support, revealing that she loves just how feisty some of them can be.
"I have the best fans in the word," she said. "They are feisty, dedicated and they'll look after me. It's crazy that they have taken that time out to support me, but I'm so grateful."
Meanwhile Abi's fellow Girls category contestant Tamera Foster has hit back at claims that she is a 'diva' backstage.
The 16-year-old said: "I treat people the way I like to be treated - and that's well.
"We are here in a working environment and I don't want this experience to come crashing down around me. I just try to make it all as fun as possible."
She added: "I don't feel like a star at all. I'm still learning so much. I'm not sure I will feel like one until I'm really up there, and I mean up there like Rihanna. I won't feel like a star unless I reach that kind of status."
The remaining seven contestants will return to the X Factor stage this week to perform songs from the 'Great British Songbook'.
The X Factor returns to UTV on Saturday and Sunday from 8pm.