Only five of the 20 Premier League managers are English and that figure has only increased in the past week when Kevin Ball replaced Paolo Di Canio in an interim role at Sunderland.
Bruce feels things need to improve after acknowledging the frustration that a lot of top jobs are handed to foreign coaches.
"Jamie Carragher would be someone who I thought would go into management as he has something to offer, he is full of enthusiasm, he is a football nut, usually they are the ones who you think is management material," he told Sky Sports News.
"But now, with the failure rate and the time it takes for exams and to pass your badges, there is a big myth out there that it is a big merry-go-round, one or two don't get back on, they have a crack at management and it doesn't quite work out but they are never to be seen again.
"So we must encourage the young British manager and of course I am delighted that Man United went for Moyes, there is someone who has been terrific.
"It is a frustration for us all that all the big jobs seem to be going for the foreign coach and I have got nothing against that, but we must find a way to encourage young British coaches if we can as we are never going to produce a great manager again if we are not going to give them a chance."
You can hear more from Steve Bruce with Tom White on Weekend Warm up from 6pm on Sky Sports News.
My favourite British bosses are Les Reed and Chris Hutchings.- tk421