Carragher wrote in the Daily Mail: "It has been the week from hell for David Moyes, the lowest point of a season in which his dream job became a nightmare.
"But the support for him to turn things around for Manchester United should not be limited to those within Old Trafford. Every British coach and manager should be firmly behind Moyes, hoping he is successful.
"Why? If Moyes fails, it will be a long time before a British coach is considered for one of the top jobs. Harsh though it may sound, it is the truth. Foreign owners won't be prepared to take a plunge on those who have been 'homegrown'.
"Moyes is at the forefront of a crucial period for our coaches. It has not been a common theme in the modern era that, as now, the three biggest jobs in British football - United, Liverpool and England -have simultaneously been held by managers from these shores.
"You have to go back to mid-1998, when Alex Ferguson was joined by Roy Evans and Glenn Hoddle, so it will be intriguing to watch how Moyes, Brendan Rodgers and Roy Hodgson go about achieving their aims.
"Make no mistake, they are all under pressure to deliver."
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