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 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."
"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," 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."
- Manchester United