"We have played by the same rules as every other person trying to get a spot in MIQ and most have better reasons than we do for getting a spot and that is the way it is. It's a lottery and our numbers haven't come up."
Murphy and Stanaway were to race as a wildcard entry and still hope to compete in the 2022 edition with the backing of Boost Mobile boss Peter Adderton.
"We did everything within our means to make this happen and I am so bitterly disappointed that it is not to be. I also want to thank the many fans who have reached out both publicly and privately not just to express their support but also to see how they could help," Adderton said in a statement on Friday.
"It shows just how special this would have been, which is why we will do everything possible to make this happen in 2022 instead."
Meanwhile, in a desperate bid to ensure he does not miss the Bathurst 1000, fellow driver David Reynolds went to Homebush on Monday to have the vaccination after learning that his exemption was in doubt.
The emergency dash to have his first shot should ensure that he will be cleared to race at Mount Panorama on December 3.
"I want to thank Kelly Grove Racing and all of our fans and sponsors for their support," Reynolds said. "And I can't wait to get back behind the wheel at Bathurst."