The Belgium international striker arrived for a £28 million fee during the close-season after spending a successful loan spell with the club in 2013-14, which came following a temporary stint at West Brom.
Reportedly unhappy about a lack of chances at Chelsea, Lukaku made the permanent switch to Everton and Martinez is under no illusions as to whether the former Anderlecht star was worth the hefty fee.
Scored his first Premier League goal of the season in Saturday's 2-0 win at West Brom and Martinez was left delighted by what he believes is the perfect forward for his team.
He said: "When you bring a player in the club it's always a gamble, but in this case it wasn't a gamble at all because we had the advantage of working with Rom for a season.
"For us it was very important that we could keep him at Everton. I always felt he developed a very homely feeling with his work at Goodison [Park].
"I think his relationship with the fans is quite unique. As a player he is everything you'd expect as a striker.
"He's young, he's got the mentality that we want to have as a team. He wants to achieve, wants to win, he works extremely hard and he has absolutely everything. [He's] strong, good with the ball, a clinical finisher with right and left [feet] and he is still only a young man.
"Money can be spent in many ways, but I didn't mind the sum because I knew it was money well spent."
The match saw Everton not only pick up their first Premier League win of season, but it was also their first clean sheet in all competitions, and Martinez was relieved to bounce back from conceding six at home to Chelsea before the international break.
He added: "We'd been focusing a lot on what we wanted to do on the ball and trying to break teams down. The focus has been on that in preseason.
"We went to Leicester [City, for the first game of the season] and we were very good for the entire game and then in the 86th minute a deflected shot ends up in the path of the Leicester striker and we lost our confidence a little bit.
"It was vital to get that side [defending] of the performance right. We showed both sides really well."
