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He also revealed what he believes was the Springboks' trick play which fooled England before they even kicked off in the final.
In a lengthy interview from Japan with Newstalk ZB's Martin Devlin, Smith - who was a key lieutenant for World Cup-winning coaches Graham Henry and Steve Hansen - said the public and media had underrated the All Blacks' ability to get up game after game during a golden decade.
But cracks had started to appear before the World Cup, with mounting losses and the retirement of seven greats after the 2015 triumph suggesting "there were going to be some tough moments".
Smith, himself a former All Blacks head coach, picked out a key tactical ploy which he believes backfired on the All Blacks as they were smashed by England in Yokohama.
"Whilst we played outstandingly against Ireland [in the quarter-final], the tactical plan that day worked because those outside backs from Ireland rushed up with out-to-in defence all the way to Anton Lienert-Brown in the midfield," he told Devlin.
"This gave the All Blacks that relief zone out wide through cross-field kicks or passing over the top but unfortunately the English watched that game too and they had a defensive plan that countered that attacking strategy. Therein lay the issues I think.
"Essentially from what I understand - I'm not close to the environment anymore – and through reading and looking at stuff, that plan of having two All Black forwards standing up flat and then passing way behind them to the 10 who then played wide, was put together for teams like Ireland rushing up, and gave them the chance to outflank them.
"Those two forwards are the players you generally rely on to keep the ball alive in the tackle. They would take the offload or make the cleanout to give you the lightning-quick ball you are after."
Instead, Smith said, the All Blacks had to rely on slow possession - a key contributor to the surprise defeat.
"But because they were 10m ahead of the attack they were late arriving to all those breakdowns. It gave us slow ball and didn't really give us a chance to keep the ball alive. It probably was the reason we lost so convincingly," Smith told Devlin.
"Everybody talks about us losing the gain line – we clearly did. We got tackled 10 or 15m behind the gain line probably nine times in the game. From that we got slow ball or lost the ball. But that's the reason – those forwards were out of the game and not able to give any support.
"Also [England assistant coach] John Mitchell had their defence numbering up from the outside so rather than rolling the dice and everyone rushing in to make the tackles, generally - although not all the time – they had that outside man-marked.
"It took away the cross-field kick and our ability to pass over the top, which put us in trouble. We didn't have any solutions to it and kept getting smacked behind the lines."
The All Blacks weren't able to change to Plan B after the halftime break, Smith said.
"So can you change? Yes, you can change. They came out from halftime and changed the pattern, we hit shorter and tried to penetrate in closer. But as with any tactical plan, it's stuck in the brain and it's pretty difficult to get wholesale changes.
"That's what happened – we went back to moving it wide in that second half and it just didn't work."
Smith also believes South Africa used the warm-up period before the final to fool England by having their halfbacks Faf du Klerk and Herschel Jantjies put up a stream of high kicks.
"[South Africa] showed in the final they were the best team in the tournament because they were able to adapt," he said.
"They changed from kicking every second ball to actually playing some footy and using the skills they've got.
"It was a clever plan – I watched de Klerk and Jantjies warm-up and they did half an hour of box kicking with the English coaches watching them. They didn't practice a pass, yet seldom boxed kicked [in the game]. They sucked a few people in before the final."
The full interview with Wayne Smith airs on The Devlin Radio Show on Saturday.