The Boks were beaten 49-0 in Brisbane last Saturday - their second heaviest defeat in their history - with several pundits already calling for White's head.
"Sometimes you get it wrong, and when you get it wrong it can go badly wrong," White told reporters.
"We really had the good times and now it's time to reflect and understand what is happening.
"We are embarrassed by what happened on the weekend and the only way out is to learn from it and move on. If not, we've got to be accountable."
The coach admitted he had done a lot of soul-searching since the defeat and believes drastic changes would be unwise ahead of Saturday's match against New Zealand in Wellington.
"At club, colts or school level, I have never had to endure the things I saw on Saturday," he added.
"There is no book saying 'go to chapter six and this is what you say to your players'. But the reality is, as a group, we hold the jersey proud and now we have to make the right decisions.
"If I say it is wrong to change it now, or if I say why not change it against the best team in the world, I will be wrong. I know where we went wrong, but we can't make too many changes now, in the midst of the competition.
"It's difficult to change so quickly, but we have practices on Tuesday and Wednesday to try things and see exactly where we are.
"Only in time will we know whether it can work in a game. But we've got the technology, the coaching staff and the expertise to analyse and make sure we adapt."
Meanwhile, Sharks coach Dick Muir applauded the call for veteran fly-half Butch James to join the squad.
James could well play against the All Blacks after arriving from South Africa on Tuesday and Muir believes he is the perfect man for the job.
"Butch is the man for this type of situation the Boks are in," Muir told the Mercury.
"His aggression, confidence and skill lift a backline, and he is the kind of character that relishes tough situations. He is very excited about his call-up and we are very excited for him. He will do a great job."