Everton boss Dyche, who has previously managed Watford and Burnley, was asked recently about the lack of British bosses in the Premier League.
"I have never felt any differently - if you are good, you are good and if you are not deemed good enough then you are not," he said.
"Results usually indicate that journey and the amount of foreign owners in the Premier League means it is no surprise you have a lot of foreign managers.
"It has never bothered me and if you are good enough to get the job you will get it.
"Unfortunately a couple of managers have lost their jobs. It is very difficult, I can assure you of that and I wish them well whatever comes next. Results are eventually what costs all managers, no matter where you are from on the planet."
So should English managers be looking at moving abroad - as their international counterparts often do?
The only English managers working in Europe's top leagues are Liam Rosenior at Strasbourg and Will Still, who was born and raised in Belgium and is in charge at Lens.
Appleton, who has spent his career to date in England, said: "It's almost a double-edged sword.
"Obviously if we can't speak the language, we're unlikely to get the opportunity and then, because we probably know that we're going to lack opportunities, we probably won't apply or put ourselves out there.
"The frustration is I don't see a Spanish or Portuguese or French, even some of the Scandinavian [clubs] taking British coaches as seriously as their own.
"That's probably a little bit down to the factor of how big the Premier League is and the quality of players that come over.
"It's almost like we've created a situation where, because of how big the Premier League is and how worldwide is it, it has been a bit of a detriment to some of the opportunities that British coaches need."