The 21-year-old joined the Glovers on loan from Premier League outfit Southampton on the Friday prior to the tie with the Bantams and was handed a start by manager Darren Way at the first opportunity.
Barnes repaid Way’s faith by netting the hosts’ opener with a cool finish just past the hour before Jordan Green sealed progression with a well-taken strike.
The young forward received a standing ovation when he was substituted on 85 minutes and described the day as ‘a great feeling’ after a whirlwind 24 hours.
He told iFollow Glovers: “It all happened really fast. I went to training with Southampton on Friday and I got pulled by my gaffer who said ‘how does Yeovil sound?’ and I took the opportunity with both hands.
“I want to play first team football and score goals, so it’s the perfect place for me to be.
“It hasn’t really sunk in (that I scored) and probably won’t until I watch it back!
“For me (the goal) was instinct; I try and look at the keeper and assess the angles and if there isn’t one then through the legs is a great option. I chose to do that and luckily it paid off.
“There are different finishing techniques and when it comes to that situation, that’s when you put your practice into perfection and it paid off in that moment.”
Barnes continued: “The fans were brilliant. They were always behind us and I’m glad we gave them something to celebrate.
“It’s an incredible feeling (to be in the hat) and regardless of who we get we can be giant killers and put in a great performance again.”