The Proteas need to draw or win the clash in Port Elizabeth, otherwise they will succumb to a first Test series loss since 2009.
Cullinan, writing in The Times, suggested Johnson exposed "mental fragility and poor techniques" and that it was unlikely the issues would disappear in four days.
"One doubts the Proteas will have time to recover and find a way to compete in the remaining two Test matches," Cullinan said.
"South Africa will have to play better cricket than Australia to win the series.
"But where that is going to come from at such short notice is anyone's guess.
"Can the Proteas find hearts and techniques to deal with Johnson ... I doubt it."
South Africa captain Graeme Smith, speaking after a 281-run loss at Centurion, pointed to the fact the Proteas quickly bounced back from poor results that opened their past two Test series as cause for confidence.
The Proteas were held to a draw in their first Test against India at home last year, and were belted by seven wickets in the first clash of a two-Test away series against Pakistan in October.
Cullinan noted the current visitors were a vastly different beast.
"In recent Test series we have become accustomed to slow South African starts, which we have gotten away with against lesser opposition," he said.
"It's highly improbable it will happen this time around because Australia are far too organised and confident."