The Scot was appointed at Manchester United last summer but was sacked after just 10 months as the reigning champions finished seventh and failed to qualify for Europe for the first time in 25 years.
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"To do a top job, I believe you have to earn your stripes," Moyes told told reporters.
"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."
Moyes has highlighted the work of both manager-of-the-season winners, Rodgers and Crystal Palace boss Tony Pulis, and hopes others are afforded the chance to impress in future.
"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."