The former Chelsea striker admits he's been amazed by the support he's received in Naples.
Recalling his goalscoring debut against Parma, Lukaku said: "I was overwhelmed, it was all so incredible. I felt a different atmosphere with a really positive energy. Yes, I scored, but we won, which is the most important thing. As a player now I take things day by day.
"I try to give a little bit more every day and see where it takes me by the end of the season. As we say in English, this is my mentality. I try to give more than yesterday every time."
Asked about the move, Lukaku continued: "When the news of the contact came out... I'm a person who looks at Instagram a lot and there were a lot of messages from Napoli fans. Then I spoke to (Dries) Mertens, who I've known since I was 17. I already had a trusted friend who was preparing me for life here. You can see that you represent an entire city and its people.
"It's fantastic to experience. It gives you energy to give your best every day. When you see the players, the physiotherapists, the waiters, and everyone who works here, they are all true Neapolitans who love the club. This makes you feel good but there is also a great responsibility to give your best."
Asked if he's learned any Neapolitan, Lukaku laughed: "No, but when I go to the physiotherapist in the morning I try to understand what the kids are saying but it's hard, I'll get there little by little. Give me a couple of months and then I hope to have a chat with someone when I go to the supermarket, who knows!"