Johnson is thought to be considering his future after a tournament when England stuttered through the pool stage in New Zealand and then crashed out to quarter-final opponents France.
But their stay in New Zealand was overshadowed by players' raucous behaviour at a bar in Queenstown, before three players - Chris Ashton, James Haskell and Dylan Hartley - were forced to apologise to a female hotel worker in Dunedin for lecherous comments.
And then centre Manu Tuilagi was fined £3,000 by the Rugby Football Union for diving off a ferry into Auckland Harbour as England's wretched stay in New Zealand drew to a close.
On the field, England performed with little ambition or adventure, grinding out narrow victories over Argentina and Scotland before exiting the competition against a limited French side.
It not only raised questions about Johnson's future, but those of his coaching staff, while several England stars could easily have played their last games for their country.
And Carling, who captained England 59 times during his 72-cap career, said: "I don't know if Johnno will put himself up again, whether he will actually even put his name in the hat.
"I personally think that even he would be hard-pushed to say the coaching team should stay.
"He's a very loyal man and if he is told the coaching team needs to change, would he still hang around? I don't know."
Carling, speaking in Auckland in his capacity as a Heineken World Cup ambassador, added: "I also think Johnno is all about winning.
"He was an incredible player, he was an incredible captain, and if you sit down and assess the last three and a half years, has it been good enough?
"Have England progressed far enough? Personally, I don't think they have."
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