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But at the same time, Castle said the governing body "can't just ignore" the team's below-par performances across the first two Bledisloe Cup tests.
Castle is set to meet with Cheika later on Tuesday to discuss Australia's form and what more needs to be done to bridge the ever-growing gap between the Wallabies and All Blacks.
Castle name-checked defence as a problem area, potentially putting assistant coach Nathan Grey in the gun after the Wallabies leaked 78 points in their Bledisloe Cup defeats in Sydney and Auckland.
But Castle said there was no prospect Cheika would be sacked before the end of his current deal, which runs out after the 2019 World Cup.
"He's contracted through to World Cup. He's got a plan, we're across that plan, we're comfortable with it," Castle told reporters in Brisbane on Tuesday.
"But clearly, you can't just ignore the performances, they're not acceptable.
"So it's about what can we do to support him as an organisation to make sure he's got what he needs to make sure the Wallabies are successful as we lead into that World Cup.
"Certainly from our perspective, the board and myself, our support's behind Michael Cheika."
Castle said Rugby Australia would explore if Cheika and his coaching staff needed "extra support" to improve their on-field prospects.
But after full-time assistant coaches were introduced for the first time this year and a trial match arranged to blow out any pre-Rugby Championship cobwebs, it's hard to imagine what more could be done.
"There's different parts of the game we haven't performed, particularly around our defence, and that would be something that we'll be having a conversation about," Castle said.
"I don't think it's about changing what we've got, it's about what can we bring. We've got a wide rugby community that's had significant success on the world stage.
"What can we use in those experts that are proud Australians that want to help the Wallabies to make sure that we can continue to be successful?"
Australia haven't won the Bledisloe Cup since 2002.
"It's hard, because we all want to beat New Zealand. That's the reality. They're the benchmark, they have been for such a long period of time," Castle said.