It takes a certain type of person to become a manager, many love the game and stick to coaching - either at community or youth level to give back and become mentors like someone did to them. If there is a problem with black coaches getting their chance as managers then it needs addressing, however it doesn't appear from the outside that there is anything obvious.
Under-represented, sure, compared to, say, the proportion of black players in the leagues, but this in itself isn't an indication of racism and the proposed 'Rooney Rule' thing from NFL doesn't automatically fix this.
To decide properly, first we should see stats like 'applications vs interviews', 'interviews vs hires' and who else applied. Not just how many clubs have black managers, it's too simplistic. If Paul Ince applied for Chelsea and so did Jose Mourinho but they went with Jose, that isn't going to be because of skin colour. If 100 black coaches applied and 0 got interviews, that's an issue perhaps, but we don't know...
Players who retire and go into coaching, but not all. So should we expect more black coaches in the future? with the money in the game maybe there's no need to stay employed and ex-players are happy to enjoy their life after football.
A few years ago thee was a horrendous stat about how many coaches in the UK have all of their qualifications. Really not that many, in all honesty. Moans about going for a foreign manager over an English one, when the English one doesn't have the required badges and the foreign one does. More should be done by the FA, but first to make sure every coach is up to standard first, level the playing field, and then see whether there is a discrimination problem.