White took the Canberra-based side to the final of the southern hemisphere competition this season and had two years left on his contract but quit abruptly last month to return to South Africa where he has been appointed director of rugby with Durban's Sharks.
White had been in the running to succeed Robbie Deans as head coach of Australia after the New Zealander was moved on in the wake of the British and Irish Lions series loss, but former Queensland Reds coach Ewen McKenzie was preferred despite having no experience at test level.
White, who guided the Springboks to the 2007 World Cup win, told Fairfax media he had become "disillusioned" with the Brumbies job after being overlooked for the Wallabies.
"I told (the Brumbies) I was feeling disillusioned with where my career was going in Australia," White said in comments published on Friday.
"And who says I can't coach Australia after the World Cup? I've not turned my back on Australia.
"I don't feel guilty at all about wanting to chase an international dream, players do it all the time."
White, who helped turn the Brumbies from cellar-dwellers into contenders in his two years in charge, said he had felt "heartsore" to leave.
"I know that in my heart I did my bit and I gave my 100 per cent and there was no malice or skulduggery," he said.
"The bottom line is I just wanted to move on. Families allow family members to move on. It happens. A lot of the guys I've spoken to, they all understand why it had to happen."
White's walk-out left the Brumbies with two caretakers in charge in assistants Laurie Fisher and former Wallaby Stephen Larkham. The club has little prospect of finding a replacement from outside the club with pre-season training already under way.
White will return to Canberra in May when the Brumbies host the Sharks.
"I will enjoy it," he said. "I'll catch up with a lot of my friends that I've got in Canberra. It's not like I'm sitting here in trepidation thinking I'm going to have to go back to Canberra," he said.
(Writing by Ian Ransom; Editing by Patrick Johnston)
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