Lukaku failed to find the net at the Rostov Arena on Monday, but was among the protagonists as his dummy allowed Nacer Chadli to tap home the winner from close range well into stoppage time.
It was not the first time the former Anderlecht prodigy made an impact this tournament, having scored four times in his opening two games in Russia.
Assistant coach Thierry Henry has been credited for Lukaku's fine run of form for the national side and even though Martinez admits the Arsenal legend has played a role in the Belgium No.9's sublime performances, he is adamant the improvement is down the forward himself.
"I think Thierry deserves huge credit. He has been working really well with Rom," Martinez said in an exclusive interview with Goal ahead of Friday's quarter-final clash with Brazil.
"But I think Rom is a player we know well because as a young man we saw his outstanding talent. His outstanding talent is the goalscoring ability that he has. When you see him at the age of 19 coming into the Premier League and making the impact he had with West Brom and seeing that slowly he was adapting to playing 90 minutes.
"He comes to Everton and you can see that mindset of a winner. Elite brain of wanting to become the best in his position. You see an evolution on the footballer.
"But it was significant to see someone that from the outside many people could say, well he would accept if you see a selfish action of Romelu Lukaku on the pitch because you are in front of goal and maybe you are hoping to score a goal.
Martinez: Unselfish Lukaku has an elite brain
More than a goalscoring machine... Belgium boss Roberto Martinez has paid tribute to Romelu Lukaku's maturity as a footballer after his stepover for Nacer Chadli helped his side reach the World Cup quarter-finals. (Peter Staunton) #BEL #WorldCup Posted by Goal.com on Thursday, 5 July 2018
"I think his decision of assisting that ball to someone who is in a better position speaks volumes of his maturity and his understanding of why we are here – to be a team, to help each other, to try to win games."
Lukaku has netted an impressive 40 goals in 72 appearances for Belgium to become his country's all-time top goalscorer, 23 of which came under Martinez.