The tourists headed into the ongoing fifth and final Test at The Oval in south London having already surrendered the Ashes at 3-1 down in a five-match series.
There had been speculation that with The Oval clash a 'dead' rubber, Australia would recall 22-year-old fast bowler Pat Cummins in place of the injured Josh Hazlewood.
Cummins made a sensational debut, taking six for 79 against South Africa at Johannesburg in 2011 but fitness problems mean he has yet to make his second Test appearance.
However, Cummins was left out at The Oval, with Australia opting instead to bring in Peter Siddle for the 30-year-old Victorian's first Test of this series.
Leg-spin great Warne, commentating for Sky Sports, said both captain Michael Clarke and coach Darren Lehmann wanted Cummins in the team but had been overruled by Marsh.
"By all accounts, the word on the street it was his call," Warne said.
"The captain and coach and everyone wanted Pat Cummins to play.
"But Rod Marsh as chairman of selectors flexed his muscles and said 'I want to play Peter Siddle'."
Warne added that Marsh, an outstanding wicketkeeper/batsman in the successful Australia side of the 1970s, had "got it wrong" in opting for the experienced Siddle over Cummins.
"That's just common sense for Pat Cummins to play this Test," Warne said. "They've made some silly decisions.
"Sometimes that happens when you're losing, the panic starts."