Martinez's men have yet to lose in the Premier League so far this season, but have taken just three points from as many games after draws against Norwich City, West Brom and Cardiff City.
Everton have netted in only one of those games, as Ross Barkley and Seamus Coleman scored in the 2-2 draw at Carrow Road on the opening day of the campaign.
Since then, though, Martinez's side have struggled in front of goal, but the former Wigan Athletic boss is confident that the Belgium international - signed on a season-long loan from Chelsea on the final day of the transfer window - will provide the impetus his team needs.
"I think it's fair to say that our opening three performances in the league have been really, really good, but all they have been lacking is that goal," Martinez told the Liverpool Echo.
"The fans realise that and when you see a player arrive who is capable of doing that it excites you.
"He (Lukaku) could be that little piece which completes the puzzle."
Martinez recruited heavily in the close-season as he aims to keep Everton in the upper echelons of the Premier League, bringing the likes of James McCarthy, Gareth Barry and Arouna Kone to the club.
And the Spaniard believes Lukaku, who scored 17 goals on loan at West Brom last term, is an ideal fit for his team.
"We are all excited about Romelu, without forgetting that Nikica Jelavic and Arouna Kone are very important for us too, but extra competition for places is also important," Martinez added.
"I wouldn't say it was a coup signing him, it was a perfect fit for what we needed.
"Romelu is perfect for what we were looking for.
"He's not going to need any settling period in the league, he knows it inside out.
"I see him as someone who can come in straight away and hit the ground running."
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