The 24-year-old completed a £75m move from Everton to United over the summer and has had an instant impact, scoring five goals in five Premier League games so far.
Martinez knows Lukaku well, having brought him to Goodison Park from Chelsea in 2014, and has witnessed "a big difference" in the player in his new role as Belgium national team boss.
"It never crossed my mind that it would be something difficult for Rom," Martinez told talkSPORT of Lukaku's switch to United. "Everyone that plays with him or works with him realises very quickly that he has an elite brain.
"As a footballer, you can have your attributes but the focus he can have is quite unique. When he went to Manchester United he was solely focused on starting well and making a big impact and that is what he has done.
"He is still a very young player - sometimes we forget he is only 24 - but his goalscoring record is sensational and he is a player that wants to carry on developing and carry on learning. Now he is with a manager with whom he will keep learning different aspects at club level.
"I have seen a big difference in terms of his maturity when he comes to international camps. From the young player I signed from West Brom and Chelsea at that time, it is the same goalscorer but with an incredible maturity. That is great to see and he still has many, many years to develop."
Belgium are the only European country to have secured their place at next year's World Cup through qualifying so far.