The singer and guitarist cursed at the audience after the band's performance was not well-received, before further berating the crowd on Twitter days later.
He told BBC 6 Music: "After we finished the tour [in 2009], after we went home, after about three weeks, I came to terms with it and I was proud of what we'd done.
"I wanted to do some interviews and just apologise for my attitude. We took it out on a lot of people, me particularly, I took it out on audiences. I forget which festival it was - was it Reading? - where we had a big backlash."
Followill, 28, added: "I took it out on the crowd, and at the end of the day it was probably our fault. Because of the success I expected everyone to [cheer] for everything we did.
"That was my Kurt Cobain moment when I was hating the success and I was scared that people were thinking that we did this on purpose, that we made this record (2008's Only By The Night) so that it could be big."