Spanish striker Llorente signed on at Stadio San Paolo two months after the end of his contract at Tottenham.
The 34-year-old has prior experience in Italy, having scored 23 Serie A goals in a two-season stint with Juve.
Llorente won the Scudetto twice during his time in Turin and knows toppling the Bianconeri is a tough ask.
"It's not easy. When I was at Sevilla we beat them 1-0 [in 2015], with me scoring," Llorente said.
"I've beaten them before but it's one thing to do it in a single game and another thing to do so over the course of a season.
"As I've said, I'm confident and I believe we can have a good season.
"There's a desire to win a trophy, but we can't put pressure on ourselves. Juventus are the ones with all the pressure. They have a very strong bench.
"We have a very talented group with young players who will develop. I'm sure that we'll have a team of top players in the future."
Napoli have scored seven goals in their two games this season, including three in a thrilling defeat to Juventus, with the diminutive Dries Mertens at the point of attack.
Llorente presents an entirely different option and while playing time might not be immediately forthcoming, the former Athletic Bilbao striker is no less enthused about working with esteemed head coach Carlo Ancelotti.
"It’s a great feeling when a coach like Ancelotti calls you," he said.
"I was already keen on coming to Napoli, but when there’s such a successful coach involved you have no doubt that you’re making the right decision.
"Napoli is a big club with a great coach. I really wanted to work with Carlo so I’m delighted to be here."
The Partonopei will get their Champions League campaign underway on Tuesday when they welcome reigning champions Liverpool to the San Paolo.
Llorente discussed facing the side he and his Tottenham teammates lost to in last season's final.
"It is a really strange feeling because not so long ago we had a big disappointment after losing the Champions League final, something that was really painful.
"It is the second time that happened to me. Also, against them I played one of my best games when I was at Swansea. I scored two goals at Anfield and we won that game 3-2 in my very first game at Anfield.
"Now we have this game, so I need to continue doing well against them."