Agriculture Minister Barnaby Joyce told Australian public broadcaster ABC that Depp "looked like he was auditioning for the Godfather" in the somber apology video, but said he did not "think he'll get an Academy Award for his performance."
He doubled down on his criticism in an interview with CNN affiliate Channel 7's "Sunrise" program, advising the Academy Award-nominated actor to "do it again" with "a little gusto."
The apology video by the Hollywood couple was played to a Queensland court on Monday as Heard appeared over the incident.
Heard, an actress who has appeared in films including "Magic Mike XXL" and "The Danish Girl," was spared a conviction when she pleaded guilty to knowingly producing a false or misleading document, while two other charges of illegally importing her dogs were dismissed.
The court magistrate gave her a one-month good behavior bond sentence, Channel 7 said. If she breaks the bond, she will have to pay a fine of 1,000 Australian dollars ($767), but the incident will not go on record.
Joyce happy with video's message
The celebrity couple's woes began when they landed in Australia aboard a private jet last April for Depp to film a "Pirates of the Caribbean" movie, without properly declaring the dogs' arrival.
Joyce gained international headlines at the time when he issued a 72-hour ultimatum to the couple to get the dogs out of the country.
"Mr. Depp needs to take his dogs back to California, or we're going to have to euthanize them," he said at the time.
On Wednesday, the politician told ABC he was pleased the video was spreading a broader understanding of Australia's laws to an international audience.
"At the end of it we've got a message that is going all around the world right now. It's going off like a frog in a sock telling people that if you come into this nation and you don't obey our laws, you're in trouble. That's what this is about."
Heard: 'Protecting Australia is important'
In the video, released by the Australian government, a stony-faced Heard sits alongside Depp to state she is "truly sorry that Pistol and Boo were not declared. Protecting Australia is important."
"Australia is a wonderful island with a treasure trove of unique plants, animals and people," the actress said.
"Australia is free of many pests and diseases that are commonplace around the world. That is why Australia has to have such strong biosecurity laws."
Depp added: "Australians are just as unique, both warm and direct. When you disrespect Australian law, they will tell you firmly. "
"Declare everything when you enter Australia."
Depp was not charged over the incident but accompanied his wife to appear at the Southport Magistrates Court on the Gold Coast Monday where they received a red carpet-like reception.
The two were besieged by media although police were on hand to keep things under control.
Heard's defense team described the Pistol and Boo "saga" as a "tired, terrible mistake."
The actress said she was "distracted" when filling out the immigration forms upon her arrival, but the prosecution countered that it was "no excuse" -- Australia's famously strict biosecurity law "applies to everyone."
According to 7 News, Heard's assistant was responsible for the dogs' travel arrangements and was dismissed after the incident.
The illegal import of animals carries a maximum penalty of 10 years in prison and a fine of 102,000 Australian dollars ($75,000); the false document charge has a maximum penalty of a year in prison and a fine of 10,200 Australian dollars ($7,500).