Kone was booed by the Everton supporters last season but appears to have won over the Goodison Park faithful after scoring a hat-trick for the Toffees last weekend.
Speaking to Sky Sports, the Ivorian discussed how he is grateful to Martinez for showing faith in him during his layoff with injury.
Kone said: "Obviously Roberto brought me with him from Wigan, and I think that having worked with him before has really helped."
"Throughout the tough periods, he kept having conversations with me, reassuring me and never at any point did he rush me to come back."
"I think his confidence really helped me in terms of getting me back to where I am. So now, it's really important that I try and pay him back for the confidence he's shown in me for the rest of my time at Everton. I don't think I'm at my absolute top level yet. I don't think I'm far off though."