Rodgers led Liverpool to second place in the Premier League last season and also brought Champions League football back to Anfield.
Pulis took Crystal Palace from seeming relegation to an impressive mid-table finish and Moyes is happy that British managers are getting a fair crack of the whip – which has not always been the case.
“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 said.
“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.”
Moyes, who spent 11 years at Everton before his ill-fated spell at United, added: “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.”