But White, who has installed Bob Skinstad as captain for the two games, insists the World Cup is his priority.
"I find it odd that I'm not allowed to take this squad overseas," White said.
"We have to look at the bigger picture in a World Cup year and, besides, there are only three new caps in the squad.
"For the record, the best players in the 1999 World Cup, which Australia won, were John Eales and Tim Horan and neither of them played any Super 12 rugby that year.
"Last year, New Zealand played an A and a B side. Nobody said anything in 2004 when I fielded a very inexperienced side with just 175 caps."
White also pointed out that the All Blacks had fielded two different sides in last year's Tri Nations, and nobody had complained about it then.
"Let's say the All Blacks win the competition, and they want to field a second-string side against my guys in that last game.
"Do I have the right to insist they don't rest players then and face us with a full strength side? If not, then what is everybody getting so worked up about at the moment?"
White added that his decision perhaps meant that his side would throw in the towel in the Tri-Nations to have a better chance of winning the World Cup.
He said: "If you lose a home game, it doesn't bode well.
"In a year like this, you have to make decisions that will win you the World Cup and us as South Africans are in no doubt as to how important the World Cup is - winning in 1995 changed our country.
"We have a leading sports scientist in Professor (Tim) Noakes advising us and you have to value what he says.
"He said quite plainly that we would pick up a huge amount of injuries if we used the same players to go overseas as well. As it is, we already have a lot of injuries."
White added that there was a lot to gain on this tour for the selected players.
"I believe there are about 10 World Cup places up for grabs and I believe Bob Skinstad will be honoured to lead this team as they'll be presented with an opportunity to prove themselves."
The team face Australia in Sydney on July 7 and New Zealand in Christchurch a week later.