No doubt that the small number of managers from ethnic minority communities is startling. Still, we must be careful about drawing melodramatic conslusions. It'd be interesting to contrast the number of players qualified to play for the Republic of Ireland with the number of managers from that country working in England. Certainly at EPL level there are plenty of the former and none of the latter.
Something to bear in mind about comparing English football and the NFL: the NFL is considered without rival as the foremost league in its sport. That isn't true of the EPL. An English football player or coach unable to get a break in their homeland could easily seek opportunities to prove their talent in a prestigious European league. In reality, this hardly ever happens. Meanwhile, plenty of non-English talent is able to flock to England and thrive. (The NFL doesn't have to fret about people from Abroadland taking the locals' jobs to the extent that the Professional Footballers' Association does in England). In European football there are so many avenues for talent to out, if that talent has perseverance.
Once you get a reputation for having talent, you're in clover. So many clubs are terrified that one bad season will leave their finances crippled (another difference from North America). Conseqeuently, the real prejudice in European football is in favour of the "experienced" over the untested-on and off the field.
The other matter to throw into the mix is what might be called the liberal-conservative divide in English football. This isn't predicated by race but by a person's stylistic beliefs about the game. There's a school of thought that English football tends to be unsophisticated, overly obsessed with athleticism over skill and tactical nous compared to many European rivals; that's a debate that has been going since the 1890s. Note that of the 19 current EPL managers (at the time of writing, Wolves are desperately running around the country leaving unsigned contracts on the doorstep of every practically unemployed manager that they can think of), only three are English anyway. It's possible that if a black manager suffers from prejudice, its a colourblind prejudice-that employers look upon him as just another dumb Englishman whose idea of coaching will be to yell "get stuck in" and utter the word "passion" a lot.
All of this creates a messy predicament for the League Managers' Association. On the one hand, they are trying to encourage clubs to show existing managers more patience (the typical manager gets fired far quicker than he used to), which means that they are bound to defend the 89-3 ethnic status quo up to a point; equally, the LMA want clubs to appoint less foreign coaches, which isn't legally possible given EU employment law (thanks to the quirks of English culture, the LMA forget that when it comes to football, Scots, Welshmen and anyone from the Ireland of Ireland are foreigners too); precisely how they can give special preference to coaches from ethnic minority backgrounds therefore remains to be seen.
Parenthetically, it's been a while since we had journalists wringing their hands about the lack of players from British Asian backgrounds in English football. So far, only one such fellow has ever scored in the EPL, namely Michael Chopra. He was born not in a city with a large British Asian population like Bradford; nor was he born in that sophisticated cosmopolitan paradise, London; Chopra scored his historic first EPL goal for Newcastle United and he was born in Newcastle upon Tyne-a city once described by a nitwit civil servant as being "hideously white". I'll let you take from that anecdote whatever you will about matters of race and social engineering in sport.