Highlanders boss Jamie Joseph has emerged as an early frontrunner.
In a statement sent to the Herald, Smith said he was “blindsided” by the news.
“Unfortunately, Razor hasn’t been given more time, greater opportunity to adapt and overcome many of the challenges new All Blacks coaches face,” Smith said.
“I feel sad about that - for Razor and our game.
“They obviously feel that the win % wasn’t going to improve, although that is just guesswork.”
The 68-year-old spent time in the All Blacks camp through his performance coach role with the Black Ferns and All Blacks, most recently before the Springboks test in Auckland in September.
Smith said from his time working with Robertson, he was more than capable of leading them towards the 2027 Rugby World Cup.
“I actually found Razor and his coaches to be extremely competent around their roles,” Smith said.
“Progress is often slow when you take over as a new AB coaching group. You learn as you go. Nothing truly prepares you for it.
“Coaching in this environment is becoming more and more challenging. The All Blacks’ history demands high standards, a winning attitude and innovation.”
NZR has yet to put a timeline on how soon they want to appoint a coach.
With a big year on the cards, including a South Africa tour and the launch of the Nations Cup, an appointment would be expected sooner rather than later.
Ben Francis is an Auckland-based reporter for the New Zealand Herald who covers breaking sports news.