When Moyes was announced as Alex Ferguson's successor at Old Trafford last May, the appointment was hailed as a positive sign for young British coaches seeking to reach the highest level.
However, Moyes' tenure at United proved brief and he was dismissed in April, less than 12 months after agreeing a six-year contract.
"To do a top job, I believe you have to earn your stripes," he is reported as saying by the English media.
"The route through to the top for a British manager is a long process and maybe having a job abroad and getting recognised for your work there might be the way in the future.
"But I hope I won't be the last one to be given a chance to manage one of the top ones."
"Brendan has come in and with the time he's been given has been able to turn round Liverpool and I think it's really important for British managers that he's done that." added Moyes.
"Brendan was given the opportunity and because of that Liverpool have a good future.
"Tony Pulis also showed what our managers can do (when leading Crystal Palace to safety).
"I hope I'm not the end of British managers getting opportunities at the top."
United appointed Ryan Giggs as interim manager following Moyes' departure, but have since turned to a foreign boss in the form of experienced Dutchman Louis van Gaal, who will begin his new role after coaching his country at the FIFA World Cup.
