Burger is out for seven months after sustaining a neck injury in the second Test against Scotland last month, and coach Jake White has opted not to select a like-for-like replacement in the number six shirt.
McKenzie, speaking to the Afrikaans language Beeld newspaper, claimed the role Burger plays cannot be underestimated and that the Boks may struggle without him.
"An injury to only one key player can cause even the best team to stumble," said McKenzie.
"Just look how the Wallabies struggled last season when they were without Stephen Larkham.
"I don't know whether the Springboks really know what a huge trump card they lost when Burger was injured. He is a tremendous fetcher. He gives everything, every minute.
"When I plan strategy for a match against the Stormers (Burger's club side), I always take his workrate and intense involvement into account. Any other coach probably does that.
"In Australia we attach great value to the role of a specialist fetcher. You'll find one in every Super 14 team."
South Africa, meanwhile, have arrived in Brisbane, where they will prepare for their opening Tri-Nations clash with the Wallabies on July 15.