Rae accused Petrie of presiding over the three worst results in the history of the 139-year-old club and threw his weight behind the campaign to oust him in the wake of the embarrassment of relegation from the Premiership.
Rae, speaking from his home in Corfu, said: "Rod Petrie now has to face up to his responsibility. Under his stewardship we've seen the three most humiliating results in our history.
"Managers and players all know deep down when their time is up. Surely he does too. Everyone has their shelf life."