Returning Chelsea manager Jose Mourinho allowed Lukaku to go out on loan on transfer deadline day a month ago, prompting surprise in some quarters.
That has been highlighted by Lukaku's latest brace, which took his league tally to more than all the strikers at Stamford Bridge put together.
Fortunately for Martinez, the loan agreement is for a full season so there is no chance of an early recall.
"I could be sweating now if that was the case," said the Spaniard.
He also confirmed that Gareth Barry, on loan from Manchester City, has signed a similar agreement and would stay for the entire season.
Asked whether he thought Chelsea had made a mistake letting Lukaku join another club, he added: "It will be easy to say that but you need to remember how many strikers they have.
Martinez was full of praise for Lukaku and labelled him a great goalscorer after he struck twice to sink Newcastle.
The Belgium international scored his second and third goals of the season, either side of Ross Barkley's first Goodison goal, as the Toffees routed the visitors in a one-sided first half.
Substitute Yohan Cabaye pulled a goal back within six minutes of the second half kicking off and Loic Remy's 89th-minute goal made it a more tense finish that it should have been for the hosts.
"Lukaku is a young man who has everything as a striker," said Martinez.
"Sometimes you see a number nine who is powerful and has a great physical presence - what Romelu brings is a real awareness around him.
"He is technically really gifted when he has his back to goal and that was a focal point here.
"He is a great goalscorer. He looked like a player who felt at home.
"I want him to enjoy his football, I want him to develop and become as good as he can."
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.
"I thought we were very good in the first half," he said.
"We defended extremely well and kept Newcastle to very little threat and from that point on some of the attacking play was fascinating to see the link-up play up play with Romelu, Ross and (Kevin) Mirallas.
"Once that happens you can score too many goals. Sometimes you go into half-time with a one-goal lead and that allows you to keep the tension.
"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."