The Spaniard believes the Chelsea loanee has all the attributes to become one of the finest strikers on the planet after he found the net on his return to first-team action
The 20-year-old, who started the match as a substitute after a recent chest infection, stabbed home Leigton Baines' cross nine minutes from time and his manager feels he has the all-round game to push on and establish himself amongst the game's elite.
"He can be as good as he wants to be," Martinez told reporters. "It's clear that you're not going to find another striker around the world who has that power and that strength as well as being a clinical finisher in front of goal."
"I think normally you get number nines who can take on instructions, and he's got everything. He's a young man that has got national demands and a lot in front of him.
"I respect him a lot and can be as good as he wants to be."
Though Martinez revealed he is unsure as to whether he will be able to convince Chelsea to allow Lukaku to leave Stamford Bridge permanently, he did feel the experience the forward has picked up while at Goodison Park would see him prosper in future seasons.
"Remember some players at 20 have very few experiences, but Romelu has already been an important player in Belgium before getting a massive move to a Champions League winning team," he continued.
"Then he had to find a way to be effective in the Premier League before coming to Everton where he has become a 90-minutes player in our league.
"The amount of experience he has had is similar to players of 25 years old, so I'm very impressed with the way he has developed this season. I think we are going to see a very influential player in the final 11 games of the season."
Martinez was also quick to praise the contribution of Gerard Deulofeu on his first start since returning from injury.
He said: "You need to remember it was very difficult for Gerard. He found a good level and then he got injured. I feel now he is ready again.
"He played up to 70 minutes for us and it is important to make sure he is really fully fit and strong from now until end of season.
"I am really happy with his contribution and the way he had to suffer to get that match fitness. I think we will get the rewards of that from now until May."
The Toffees were made to work hard for the points by Sam Allardyce's in-form side, and the former Newcastle United boss was disappointed that Gareth Barry hadn't seen red for a challenge in the first half.
Referee Jon Moss failed to even award a free-kick as Barry seemingly tugged Kevin Nolan to the ground as he looked to run in on goal after Carlton Cole's flick, and Allardyce was surprised the challenge went unpunished.
"There's no doubt about it in my mind. From my position, which was right behind the referee, there is no obscured view of Gareth Barry pulling Kevin Nolan down," he said.
"For me that was a key moment in the game where Kevin would have perhaps been scoring another goal because of the form he is in. He's scored four in the last five and I would have banked on him.
"By looking at it it's stopping a goalscoring opportunity and a red card, but we didn't even get a free-kick, so I'm really disappointed in that."