Fredenham highly impressed the Britain's Got Talent judges, including Cowell, on last week's episode, while she was not put through on rival show The Voice UK last night (April 20).
Tweeting about the singer's appearance on the BBC talent show, Cowell said: "Alice fredenham on the voice tonight. Confident and hopeful. Nobody turned round."
Responding to people's comments that the hopeful may have faked her stage nerves, Cowell said: "Alice on bgt. She simply lost her confidence after that reaction and she did sound better on bgt (sic).
"But to call her a fake is unfair. I was there. She was terrified. And now I understand why."
Meanwhile, X Factor host Dermot O'Leary also tweeted about Fredenham's appearance on The Voice UK, before starting a back-and-forth with the BBC show's official Twitter account.
"She doesn't want a hug. She wants them to push the button," he tweeted.
After The Voice tweeters thanked O'Leary for watching, he replied: "No sweat. You should come to one of our live shows sometime..."
The BBC show added: "We'd love to but, erm, we're washing our chairs.
@radioleary yawn. Will you judge us if we don't? Judge us with your judgey judgements?— BBCTheVoiceUK (@BBCTheVoiceUK) April 20, 2013
O'Leary replied: "Not sure any of that made sense.Nice show tonight. Just take that on face value. Still should have put Jessica Steele through."
After The Voice UK apologised for having "too much sunshine", O'Leary added: "@BBCTheVoiceUK No sweat. X #playthepipesofpeace"
Alice Fredenham recently told Digital Spy that her rejection from The Voice UK was very "disheartening".
Watch Alice Fredenham speak to Digital Spy below: