Members of the squad were criticised for their behaviour off the pitch as their leisure activities received media interest. Newly-wed Mike Tindall was caught on CCTV kissing another woman while James Haskell, Dylan Hartley and Chris Ashton were forced to apologise after making inappropriate comments to a hotel employee.
Meanwhile, their campaign ended with a 12-19 defeat to France in the quarter-final stage.
"I don't know if Johnno will put himself up again, whether he will actually even put his name in the hat," Carling said.
"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.
"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."
Wales and Australia will battle for third place in the tournament on Friday, followed by the France vs. New Zealand final on Sunday.