Kelly was grilled by Piers about her weight loss and her mum's battle with cancer a couple of weeks ago on his ITV show.
But Osbourne was pleasantly surprised by the positive response she received from the public.
She wrote in her column for Closer magazine: 'I've been overwhelmed by all the messages people sent me on Twitter after my interview on Piers Morgan's Life Stories aired. Thousands of you said lovely things, which was so nice, especially as I was really scared.'
'The point of the show is to be honest, which can backfire if people don't like you!'
The 26-year-old added: 'I was so terrified of what people would think I even prepared what I would say to fight back! But the feedback's been amazing.
'It was the longest interview I've done, and though I was discussing upsetting things I didn't want to cry the whole time - I have a great life and people would think, 'What a brat!''
Kelly admitted on the programme that she nearly got a gastric band.