After a successful 11-year spell at Everton Moyes endured a difficult season at Manchester United before being sacked in April.
The 51-year-old, who will be replaced at Old Trafford by Dutch boss Louis van Gaal next season, is keen to see more home-grown managers at the pinnacle of the game.
"To do a top job, I believe you have to earn your stripes," Moyes told several national newspapers.
"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."
Despite his time working at two of Liverpool's biggest rivals, Moyes said he is pleased that Northern Irishman Brendan Rodgers has been able to find success at Anfield.
"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 mangers that he's done that," Moyes added.
"Brendan was given the opportunity and because of that Liverpool have a good future. Tony Pulis also showed what our managers can do (having rescued Crystal Palace from relegation danger). I hope I'm not the end of British managers getting opportunities at the top."