The boyband were automatically eliminated after receiving the fewest public votes, as there was no judges' vote this week.
Band member Josh Cuthbert said: "I'm so happy with how well we've done. We've got so much to thank The X Factor for."
Jaymi Hensley continued: "This has been our dream to be on this show. Being here now, performing... I can't describe how amazing it's been."
Mentor Louis Walsh added: "I'm a little bit disappointed, but they're going to have an amazing future. They're the next big boyband!"
Union J narrowly missed out on a place in next weekend's final in Manchester, meaning that Christopher Maloney, James Arthur and Jahmene Douglas will now battle it out to be crowned winner of The X Factor 2012.
Speaking of progressing to the final, Arthur said: "I had a really bad feeling I wasn't going through. I'm over the moon, it's crazy."
Maloney added: "I'm just so grateful for everyone who has picked up the phone and voted for me and the support they've given me throughout the competition."
The X Factor final kicks off next Saturday (December 8) at 8pm on ITV1.
Photo gallery - The X Factor semi-final results: