"I think the hate [for the Knicks] has grown a little. Everybody knows how much I disliked the Knicks when I was with the Celtics, but I think it's grown to another level," Pierce said on ESPN NewYork 98.7 FM's "The Michael Kay Show" on Thursday. "I think it's time for the Nets to start running this city."
Pierce later told reporters at a Sprint H-O-R-S-E event in Manhattan: "The only thing that separates the two teams is a bridge. And both of them are in the same division and both of them are considered contenders. You can't help but say this is probably gonna be the best rivalry in sports next year."
The Nets and Knicks will meet four times in 2013-14. The first game of their regular-season series will be Dec. 5 at Barclays Center.
Both teams made upgrades in the offseason. Brooklyn acquired Pierce, Garnett and Jason Terry from the Celtics and also added Andrei Kirilenko in free agency, while New York acquired Andrea Bargnani and signed Metta World Peace.
Pierce looked stunned as he sat at his introductory news conference last month, but says he's much more comfortable now.
"I'm really settling in nicely and just embracing the change and looking forward to it," he said.
Pierce said he's a "self-motivated" person and won't be solely inspired because the Celtics dealt him after he played 15 seasons in Boston.
"I don't have to use anything to motivate me, a trade or anything like that, for me to say I want to win a championship," Pierce said. "I've only got so many more years left in my career, so ultimately the goal is to try to win another one or two, as many as I can before I retire. That's the motivation right there."
Pierce thinks this team top to bottom is the most talented one he's been on -- at least on paper. He also thinks the Nets have all the ingredients to win a championship, but it will take sacrifice.
"What team in the NBA can say they can put a starting five out there with all the guys have been All-Stars?" Pierce said, referring to himself, Garnett, Deron Williams, Joe Johnson and Brook Lopez. "That's tough. It's definitely the most talented team, but come the end of the year -- June, July -- when I'm out there on the beach, I want to say this is the best team I've ever played on, and the only way we can do that is to win a championship."
Pierce is looking forward to creating a legacy with his new team.
"I want to be that guy that says I was one of the first guys to put a banner in Brooklyn," he said.
Pierce thinks the only way the Nets can surpass the Knicks is to win.
"So I just want to instill that in the teammates, the organization," Pierce said. "This is our time. This is it. A lot of players, a lot of teams, you don't get this opportunity. It's tough. I played so many years with so many bad teams -- it's like, when you get these opportunities, you cherish them."
Pierce thinks Williams and Lopez are primed for MVP-caliber seasons.
"I think we're gonna be one of the top two or three teams in the NBA, and I see [Deron] having a great year," Pierce said. "He's gonna be thrown into that category. Him or Brook Lopez, one of them -- if not both of them."
Pierce has found a place to live and hopes to be settled in the New York City area by Sept. 1. He has talked with Garnett about the team possibly getting together in a place like Chicago or California for some workouts before training camp begins, though nothing is set in stone.
Pierce said he feels great health-wise.
"I'm as healthy as I've been," Pierce said. "My body feels great. No aches and pains. So I'm ready to go. I've been training, just started getting on the court about a week and a half ago. I got a good chance to rest and I'm ready to go."
Pierce wishes his Jan. 26 return to Boston were sooner in the regular season.
"You just want to get it out of the way. When you gotta go through something tough, I've always been a guy that just wants to get it out of the way. It's gonna be in the back of my mind," Pierce said.
Pierce added that he does not plan to go to Boston for the preseason meeting there against the Celtics.
"I'll do it just one time next year," he said.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.