Martinez arrived from Wigan Athletic at the start of the campaign before guiding the Toffees to a fifth-place finish in the Premier League table.
Coleman admits that he has thrived on a personal level while working for the Spaniard after scoring seven goals last term.
"He introduced himself to everyone on the first day and let me know his thoughts for the season and what he thought I could do," the Irishman told the Liverpool Echo. "I loved it from day one, really.
"He told me to keep going from where I left off last season and he would put his bits into my game.
"I've gone to another level in terms of goals. It's something that I was missing so hopefully I can score some next season as well."
Coleman made 41 appearances in all competitions for Everton last season.