Everton replaced Frank Lampard with Dyche at the end of last month and the former Burnley boss defeated league leaders Arsenal in his first game at the weekend.
Experienced right-back Coleman played 90 minutes in the game against Arsenal to help Everton secure their first win and clean sheet since October.
Perth pointed out that Mikel Arteta substituted Gabriel Martinelli in the 59th minute after the left winger failed to get the better of Ireland international Coleman and believes that the Everton right-back will prosper under Dyche.
The Irishman believes that the 34-year-old answered some fitness concerns and stressed that Coleman is the perfect example of how Dyche can improve good players.
“It is the first time I have seen Seamus on the pitch, where everyone said ‘he is fit enough for this level'”, Perth said on Off The Ball.
“I do not mean a lack of fitness in a lazy way; I mean a run of games.
“I think someone like Coleman will benefit from working under Sean Dyche, where everything will be done 100 per cent perfect, every stat will be analysed, set pieces will be managed.
“You have seen that Martinelli was taken off because he was ineffective and Coleman did really well, albeit Everton were sort of really defensive and there was not a lot of space behind Coleman.
“I thought that is a perfect example where you see really good players and Dyche getting the very best out of them.”
Everton are 17th in the league table and Dyche still has a tough job on his hands to take the Toffees out of the relegation zone.