Wolverhampton Grammar School student Noah Key, 15, and his band Chapter 13 earned a standing ovation during their initial audition, shown on May 11.
Judge Amanda Holden pressed her golden buzzer to guarantee the group a place in the live semi-finals.
But the band narrowly missed going to Sunday's finals during the public vote tonight.
But despite the bad news, the band said they were on a massive high after the performance of a song they had written themselves.
Amanda said: "I could not be prouder if I was your mother.
"You were absolutely fantastic. I think it's a brave choice to do an original song, but it's what you're about."
Simon Cowell said they were one of the top three acts that could have made it into the final.
"This was a million times better than the first audition," he said. "The VT showed your personalities. All you need is you, the amps, your personalities, your talent."
David Walliams said: "You could be the next big boy band."
Alesha Dixon said: "You're brilliant musicians. you're ready to go out into the big wide world."
The four-piece made up of 14 and 15-year-olds met while performing in the musical School of Rock.
Ahead of the performance, Andrew Lloyd Webber tweeted in support of the band.
The composer wrote: "Thrilled to see School of Rock alumni Chapter 13 in the Britain's Got Talent semi-finals tonight, thanks to Amanda Holden's golden buzzer! Best of luck boys."
The official video of the Chapter 13's first performance has now been seen by more than 5,600,000 people on YouTube.