"It is not just us three English ... it's all the younger managers striving to get at this level, they have got no chance of getting there," Allardyce told British media.
"We train our guys pretty well, we educate them very well, but they just need a chance.
The former West Ham United boss, who has never been relegated from the top flight as a manager, was appointed by Sunderland in October when they were 19th in the table and led the club to survival after a win over Everton on Wednesday.
"If you look across at the rest of Europe and see how many of their own they look after it's quite staggering compared to ourselves. We do not, in any way, shape or form look after our own," the 61-year-old added.
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"The challenge of the foreign managers made us better over the years, there is no doubt about that, but the way it is going, I can see no English manager in the Premier League and that could be very shortly as well."
(Reporting by Ian Rodricks in Bengaluru, editing by Nick Mulvenney)
