Roy Hodgson resigned in the wake of the 2-1 loss in Nice on Monday as his team were beaten despite taking an early lead.
Carragher, a 38-time England international, blasted the national team over what the players had developed into.
"Too soft. The more I think about England's humiliation against Iceland, the more those two words come into my mind," he wrote in the Daily Mail.
"This is what England's players have become. The 'Academy Generation' - for that is what they are - are soft physically and soft mentally.
"We saw the end result in all its gruesome detail in Nice on Monday when another major tournament ended in calamity and blame."
Wayne Rooney had given England an early lead from the penalty spot, but they found themselves behind at half-time.
Carragher said the players coming through in the youth set-up were pampered and not growing into mature players.
"I call them the 'Academy Generation' because they have come through in an era when footballers have never had more time being coached," he wrote.
"At this point I want to make it clear I am not pointing the finger at academy coaches, as others will do.
"But they get ferried to football schools, they work on immaculate pitches, play in pristine training gear every day and everything is done to ensure all they have to do is focus on football.
"We think we are making them men but actually we are creating babies."