The blonde singer admits tensions within the girl group reached breaking point last week and insists the only way they could continue was if founding member Keisha, 24, left.
Heidi - who is joined in the band by Amelle Berrabah - told Britain's The Sun newspaper: "It suddenly came to a head. Me and Amelle knew we couldn't move forward together the way it was.
"We couldn't work together anymore. But we did not want to throw away what we had achieved and split up."
Eurovision Song Contest singer Jade Ewen was swiftly drafted into the new line-up of the Sugababes on Monday (21.09.09) and within 24 hours the revamped trio jetted off to California to shoot their latest music video in the desert.
Heidi, 26, continued: "NOne Of Us were happy. We had to make a decision. Things have not been good for a few months. We tried to make it work. It's like any relationship. You try to work things through then you reach a point where you have to make a decision because life's too short."
Keisha's departure means none of the original members of the girl group - formed in 1998 - are left in the band.
Mutya, 24, said: "Obviously the Sugababes brand name will carry on, but to say there's no original member in it anymore, it just kind of puts it down a bit.
"Hooking up with the rest of the girls, I think that could be an amazing idea."