Martinez played a key role in putting in place the passing philosophy which has served Swansea so well in their climb through the leagues, before leaving to take charge of Wigan Athletic and then Everton.
Monk is very much at the start of his coaching career but has made a good early impression, picking up four points from a possible six in the league since succeeding Michael Laudrup at the Liberty Stadium.
Dyer, 26, was signed by Martinez, who he credits with helping his career take off after leaving Southampton, and can already see signs that Monk has similar qualities.
"Managers like Roberto and Brendan Rodgers have that man management skill which is key, it's massive for players," he said.
"There are always going to be players who are not playing and they need to believe they're still good players and it's about getting them to work for you.
"Roberto did that for me when I first came here. He made me feel that I was Cristiano Ronaldo, I was on cloud nine and worked as hard as possible.
"Garry is similar. I have played with him for so many years and he'll always say to me what my qualities are and that I should keep going.
"He made me believe in myself and I am sure he will do that for other players too.
"He has a lot of knowledge and has been club captain for a number of years.
"He's been involved in various promotions and he knows the game.
"His knowledge is great and he's good to work with."
Dyer is confident that Swansea can beat Everton to reach the FA Cup quarter-finals, having won the Capital One Cup last season.
"Every player wants to do well in all the cups," he said.
"To win the League Cup was amazing and now we want to win another cup.
"You can't say that playing so many games is a distraction when you've got the top teams doing exactly the same as us.
"We've just got to get on with it and make sure we can withstand the pressure."