The Belgium international scored either side of Ross Barkley's maiden Goodison goal and despite a thunderbolt from substitute Yohan Cabaye and a late prod from Loic Remy, the Toffees maintained the top flight's only unbeaten record.
Man-of-the-match Lukaku took the plaudits and Martinez admits he is pleased the terms of the striker's loan agreement ensures he cannot be recalled early by parent club Chelsea.
"I could be sweating now if that was the case," said the Spaniard, whose side moved above the Stamford Bridge club into fourth.
"Romelu is a young man who is still developing and he needs to go out on loan like he did last season.
"The next step now is taking what he did last campaign, in terms of number of starts, to another level.
"I don't think anyone questions the quality of Romelu otherwise they would never spend the money they spent at such a young age.
"We are only glad we can have him. The chemistry with the fans was terrific."
Asked whether he thought Chelsea had made a mistake letting him join another club he added: "It will be easy to say that but you need to remember how many strikers they have.
Martinez was not too disturbed by seeing his side concede twice in the second half, giving the scoreline a lop-sided look considering their excellence before the break.
"Sometimes you go into half-time with a one-goal lead and that allows you to keep the tension," he said.
"It was normal you are going to get a reaction in the second half.
"It was a completely different performance. We showed style in the first half and grit into the second."