England boss Roy Hodgson left Manchester United midfielder Carrick out of his squad for Brazil, with Jordan Henderson chosen ahead of the former Tottenham man for the deep-lying role after an impressive season with Liverpool.
While Liverpool pushed for the Premier League title, United suffered in their first season since Sir Alex Ferguson stepped down as manager, and Ferdinand suspects their seventh-placed finish probably cost Carrick his place in England's summer plans.
"He's been under-appreciated in an England shirt and never had the respect he deserves. He's the best holding midfielder England have. He knows the role," Ferdinand told the Mail on Sunday.
David Moyes was ditched by United towards the end of the campaign, and Ferdinand said: "You have to give Moyes some credit for his efforts but it was a tough year - and ultimately Carrick paid. I hope England don't suffer now, too."
Ferdinand played for England at the 2002 and 2006 World Cups, and was due to captain the side in South Africa four years ago but suffered a knee injury shortly before the tournament that ruled him out.
He said: "As a former England captain and big England fan there is nothing I would love more than to see Roy Hodgson's team reach a quarter-final showdown with World Cup hosts Brazil."
Ferdinand added: "But if I was a betting man I would not risk money on England getting out of Group D, let alone making it within sight of the semi-finals."
"I'm not damning their chances completely," Ferdinand said. "But let's have a bit of realism and accept that there are three teams in the section who have a shot at progressing, and three into two doesn't go."
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