The 20-year-old Belgium international switched to Goodison Park on a season-long loan on transfer deadline day as he seeks to get game time in a World Cup year.
He has already rewarded Everton with five Premier League goals and he has no regrets about his decision, believing he is improving as a player under the tutelage of Martinez.
Lukaku told the Daily Mail: "I made the decision. I wished them (the Chelsea players) the best of luck after I left. I'm not someone who wishes them the worst just because I am not there. They are still my team-mates.
"People want to see you on the pitch. That was why I left Chelsea. I didn't want to hear people saying, 'Hey, he's doing well in training, blah blah blah...'.
"The game is what counts. The billions watching and following the Premier League don't tune in to see you in training. They want to know what you can do in a match."
The striker added Chelsea are monitoring his progress, saying: "What we have said is private but they have been in touch.
"They keep up with my improvement. I know what I do well and what I need to improve. I want to take all those positives to make myself a better player."
The forward has praised the influence of Martinez in his development, including his approach to improving his whole game.
He added: "Roberto wants me to improve on all aspects. He wants me to be more deadly in front of goal, cleverer with my movements, more decisive and wants my first touch to improve. Everything a striker needs to know.
"He wants me to make more movements, be more aggressive, exploit my chances and be better with my passing.
"Players have good points and negative points. Some people just want to work on the negative points and forget what is good about your game. He works on everything."
A big aim for Lukaku this season is to keep up his intensity for a full 90 minutes and he is relishing the challenge.
"For the last three years I didn't have a lot of chances to complete 90 minutes," he added.
"Now it is different. I have got to work to imagine myself being ready when it is 0-0 and I am there in the 94th minute. I know in the coming weeks I will be better than I have ever been before."