Holt shocked viewers when she suddenly appeared on stage during Richard and Adam's performance on Saturday's live final.
She proceeded to throw eggs at Simon Cowell and the rest of the judging panel, while Richard and Adam continued singing. They eventually finished in third place.
The Welsh brothers told The Sun that they felt their chances of winning the show were ruined by Holt's actions.
"She said she was protesting about music not being performed properly, but we were there singing our hearts out, performing live and she ruined it," said Richard.
"She has destroyed our dream. She might regret it now and say sorry, but it's too late for us - we will never get that moment back. It's gone forever."
He added: "We just can't help but think that what she did cost us any chance we ever had of winning."
Holt has since gone on to say that her egg throwing was a protest against Simon Cowell and miming during live performances.
She said: "I basically took a stand against people miming on television and against Simon and his dreadful influence on the music industry."
Holt was backstage as part of Richard and Adam's backing orchestra. The violinist previously auditioned for the show in 2012 as part of her band Raven Quartet.
'Britain's Got Talent' 2013 final - photo gallery: