In the video Depp and his wife Amber Heard apologise for illegally bringing their dogs Pistol and Boo into the country last year when Depp was filming on the Gold Coast.
The agriculture minister says the Pirates of the Caribbean star looks like he's auditioning for The Godfather in the video that's turned into a global educational tool.
"At the end of it we've got a message that ... is going absolutely off like a frog in a sock," he told ABC radio on
Tuesday.
Mr Joyce made headlines last year when he said the dogs better "bugger off" back to the US or he'd have them put down.
The video apology was posted on his Facebook page soon after a Gold Coast magistrate let Heard off with a one-month good behaviour bond for not telling customs about the dogs' arrival.
"All around the world this is going now and people know when they come into our nation,(they have to) obey our laws," Mr Joyce told Seven's Sunrise.
He couldn't resist a jab at the actors' wooden delivery in the "atrocious video".
"Do it again, Johnny, do it with gusto, come on, mate. Rise to the camera, old trout. Rise to the camera," he joked
