"It's not in the laws of the game it's not in the spirit of the game," he said.
Pressed again, Sutherland wouldn't budge: "I am angry and disappointed. It's not a good day for Australian cricket.
"Clearly we are not at all comfortable with what has taken place. We have conducted an investigation, we have conducted reports and sanctions will be issued tomorrow and they will be significant, and they will reflect the gravity of the situation."
Co-host of Channel Nine's Today Show Karl Stefanovic was furious at Sutherland's "pathetic" response.
"Let's not beat around the bush. James Sutherland's response this morning was pathetic," Stefanovic said. "He was questioned directly about cheating as you heard and refused to answer. Questioned over and over and over and refused to answer. Why dodge it? It's cheating plan and simple. Plan, premeditated cheating.
"You know it and I know it and the ICC know it and James Sutherland knows it.
"No actual punishment was handed down this morning at a time when the game needs strong and decisive leadership. (There are) Seemingly no ramifications for the coach.
"Whether you know about it or not in leadership there's responsibility. Mistakes have been made. Admit them. Own them. Deal with them. Accept the consequences and move on.
"There needs to be a clear message sent to every player, every fan, every young boy and girl in this country who loves sport that this behaviour will not be tolerated. That message just wasn't there this morning.
"James Sutherland's response was at best weak. At worst, negligent. He must act or go."
Australian journalist Michael Best was one of the reporters who asked Sutherland if he considered what transpired "cheating" and said he was surprised the boss refrained from answering.
"I guess it's a difficult word for a CEO to say. If he says it's cheating, well, clearly the implications are enormous," Best said.
"There's a large chunk of the Australian public who think it was cheating but to avoid the question directly was an interesting move from the CEO."
It carries on from the theme that emerged when Sutherland first spoke at a press conference in Melbourne on Sunday after the scandal came to light in the early hours of Sunday morning.
On that occasion the Cricket Australia boss was repeatedly asked if he considered what the Aussies had done was cheating, but he refused to use that word.
While Sutherland wouldn't acknowledge any cheating took place, he did apologise for the hurt the actions of Australia's players has caused to the game and fans.
"I understand and share the anger and disappointment of Australian fans," Sutherland said. "On behalf of Cricket Australia, I want to apologise to all Australians that these events have taken place, especially to all the kids.
"I want to also apologise to Cricket South Africa and South African fans that this issue has overshadowed what should have been a great series."
The penalties that Smith, Warner and Bancroft will cop from Cricket Australia within the next 24 hours will be revealed via a statement, meaning another press conference won't be held and Sutherland will not have to answer more questions from the press.
The Aussies have received little sympathy for their behaviour both at home and overseas, with many in the cricket world suggesting karma has come back to bite them.
England coach Trevor Bayliss — himself an Australian — said the world has been waiting for Darren Lehmann's troops to cop their just desserts.
"I think a lot of what they're copping at the moment comes from the way they have played their game," Bayliss said, per ESPN Cricinfo.
"It's almost like teams and people around the world have been waiting for them to stuff up so they can lay the boot in. I don't think you can say when any culture has changed. It's one of those things that continually, over a period of time, builds and builds and unfortunately on this occasion it's gone too far.
"As an Australian, I'm embarrassed. Steve is a lovely young bloke who has made a terrible mistake and I'm sure Cricket Australia will work out the course of action required. It's nothing to do with us but it will be interesting to see what they come up with.
"It's not just Australian cricket that's being thought of in a negative way, it's going to be the game as a whole. Players and teams around the world have got to take a step back and have a bit of a think about the way they go about things and make sure the game continues on into the future and held in the best possible light by everyone."
