Fabio Capello's existing deal runs out after Euro 2012 next summer but after speculation that the FA would attempt to renew the 65-year-old's contract, Chairman David Bernstein stated the Italian would not be given a new deal.
Set to go: Capello is set to leave his England position after Euro 2012
In a blast at the top brass of the FA, Carragher claimed that England should always appoint a home based manager.
The Liverpool defender said: If your manager's not good enough, that's your country's fault,' he told talkSPORT.
'Get a better manager. Do the coaching qualification better. I think it's a form of cheating at international football and to be honest it's a little bit embarrassing.
'I think Capello's come into the job with all he'd done at AC Milan, and what he'd done at Real Madrid, and he's got an aura about him, a presence.
'Steve McClaren didn't have any of that coming into the job. And even if it didn't go right with him, you can't say, 'Oh, it's alright, we'll get a foreign manager now'. It's unfortunate but you have to go with the next best thing.'
Big stage: Carragher (centre) featured for England at the 2010 World Cup
The 33-year-old was persuaded to come out of international retirement by Capello to feature for England at last year's World Cup, but admitted that the Italian failed in South Africa.
Carragher added: 'Maybe it's something in our culture, or because English managers don't get the chance to win club games at the top.
'If all the Premier League managers were English then someone would have to win the league, someone would have to win the FA Cup.
'They'd have to accumulate these trophies and that's what it was like in the past.
'I've got nothing against Capello - I went with him to the World Cup and got to know him a little bit there but I just think that's what international football is.
'I can't say the World Cup went great under Fabio Capello because it didn't, but getting a foreign manager is like saying, 'Well, our keeper's not good enough so we're going to go and get Buffon from Italy', or whoever it may be.
Poised for success: Carragher claims English managers were looked over the Chelsea job which went to 33-year-old Andre Villas-Boas
Carragher also questioned the need for clubs like Chelsea to go foreign in search for a manager, claiming that English managers do not get the chance at the top level domestically.
He continued: 'Benitez, Houllier, Mourinho - they've all got things about them in terms of having won the big trophies. Does that mean English managers don't get a chance at the Premier League?
'Look at Chelsea with a 33-year-old manager. In years gone by David Moyes would have got that position, or an up and coming manager who's done a great job but that doesn't happen anymore and with the national team it's about what you've achieved, what you've got in the locker.'
Sad ending: Eriksson's last game for England saw the Three Lions knocked out of the 2006 World Cup quarter-finals to Portugal on penalties
Carragher's words come after former England boss Sven Goran Eriksson stated that the FA would take Arsene Wenger over Harry Redknapp if given a chance.
The Swede was the country's first foreign appointment to the position in 2000, and guided England to three successive major quarter-final appearances between 2002 and 2006.
And the 63-year-old backed the Frenchman for the position, stating it didn't matter what nationality the future manager is.
Eriksson said: 'People talk about Harry Redknapp as the people's choice. But I'm quite sure if the FA could get Wenger, they would take him. 'I'm sure he can do that but he's just one of the names.
'For me, it doesn't matter if he is English. Whatever nationality the coach, he has a difficult time if you don't reach the semi-finals. Quarter-finals was not good enough!'
Eriksson tips Wenger to take England role after Capello quitsHe's off! Capello will not manage England past Euro 2012, insists FA chiefHe's due to go next summer but some FA power brokers are thinking. carry on Capello