He said coach Mark Neeld had been given "carte blanche" upon taking the reigns of the club at the end of 2011, and it hasn't worked.
"There is a huge problem at the moment in that the footy department has … been given too much autonomy and there's no person there that can keep them accountable," Schwarz told his SEN radio listeners Monday afternoon.
Schwarz took at swipe at the club's chief executive Cameron Schwab who has kept a low-public profile for months during and after the tanking investigation.
"Ian Robson and David Evans have been under investigation at the Essendon Football club, but they've been on the front foot," he said.
"They can't speak about the specifics, but they can certainly talk about the rest of the footy club.
"I think as the CEO you've got to be able to put your head up, if you can't put your head up, he's not the right person for the job."
Schwab spoke on radio on Sunday following the Demon's 148-point humiliation by the Bombers, his first major interview since the tanking affair concluded.
In that interview Schwab said it was his role now to support the coach and his staff through a challenging period.
"The one thing he can be comfortable with and confident with is that he (Neeld) has got our full support," Schwab said on Triple M.
Schwarz said the gulf extends as far back as Dean Bailey's tenure as coach, citing the dumping of skipper James McDonald as an example.
"(Surely) the board or the footy director at least would have said 'no, you're not,' there are some players who you just can't do that to."
Melbourne hosts West Coast at the MCG on Saturday, and Greater Western Sydney eight days later.
Matt Thompson is a reporter for AFL Media. Follow him on Twitter @MattThompsonAFL