The Nets have dropped their last 13 encounters with the two-time defending champion Heat, losing the three meetings last season by an average of 21 points.
But before the beatings even took place on the court, Miami had already won where it matters most -- in the Nets' heads.
"I don't know if we felt we were a better team than the Heat last year," Williams said during a sitdown with first-year Brooklyn coach Jason Kidd for ESPN's "SportsCenter" conversation. "And so I think in order for us to be able to beat them this year, we have to feel like we are a better team and we can beat them. And I think we do."
Williams and the Nets face the Heat on Friday in their home opener. General manager Billy King said on WFAN on Thursday that Williams, still working his way back from an ankle injury, should see his minutes increase against the Heat, then be back to his normal playing time Sunday.
Despite the fact that Kidd will not be on the sideline due to a two-game suspension to start the season, the Nets want to show the Heat that things have changed.
"I think it will definitely be a statement game," center Brook Lopez said Thursday. "It's going to be a great benchmark for us. We absolutely believe we're capable of competing with them and that's something we're going to want to be doing down the line, obviously, in the playoffs. So we're definitely anticipating a high-energy, important game."
Not only do the Nets (0-1) believe they can challenge the Heat (1-1) for the Eastern Conference title, but they also say they are ready to turn a lopsided series into a bitter and hotly contested rivalry.
A large reason for the confidence is because the Nets have Paul Pierce and Kevin Garnett on their side now. The former Celtics have a longstanding rivalry with LeBron James and the Heat. And they are fully intent on transferring their dislike and rivalry with James to the Nets.
During an 86-62 preseason victory over the Heat in Brooklyn on Oct. 17, Pierce delivered a hard foul to James as the MVP was heading full steam toward the basket. Entering that game, there was a buzz over comments James made wondering why Garnett and Pierce didn't catch as much heat for their departures from Boston compared to Ray Allen's departure in free agency.
"Tell LeBron to worry about Miami," Garnett bristled after that game. "He has nothing to do with Celtics business. Next question."
Garnett's intense emotion toward James was punctuated with a fist pound on the conference room table he was sitting at. The Nets have taken notice and are following their new veteran leaders.
"They [Pierce and Garnett] definitely have their rivalries, their dislikes," Williams said. "As a team, if one guy has a beef with somebody, we all have a beef with them. That is how we are going to attack it this year."
That's exactly the type of attitude the Nets have been lacking against the defending champions and the exact emotion that Pierce and Garnett have been trying to instill within the Nets.
"It is not only that intense feeling toward the Heat," Pierce said recently in an interview with ESPNNewYork.com. "It has to be intense feelings toward the rest of the league. When we were Celtics, we always said we like ourselves [but] we don't like nobody. You know what I'm saying?
"That created a lot of hate for us. We were kind of like the bad guys, the big bad Celtics. We didn't mind playing the villain role. If that is what we got to do here in Brooklyn, that is what we got to do. The great teams, they create an identity for themselves. That is what we are trying to do here."
Kidd is certainly thrilled to see Pierce and Garnett change the Nets' identity from "vanilla" as he described it to a nastier disposition.
"They only know one way and that is to play hard no matter if it is against the Heat or against anybody else," Kidd said in the "SportsCenter" conversation. "No layups. They are going to make you take the ball out or make you shoot two free throws. That is the way we are going to play, not just Paul and KG, but the rest of the guys on the team."
Things need to drastically change against Miami, which is 9-0 and has beaten the Nets by an average of 17.3 points during the James, Dwyane Wade and Chris Bosh era. The last time the Nets beat the Heat was March 20, 2009.
Still, Williams senses change in the air.
"Our mentality has changed," said Williams, who played just 22 minutes due to a minutes restriction for his ankle in a 98-94 loss at Cleveland on Wednesday. "That is how you got to attack it if you want to win a championship. You got to feel like you are the best team. I am sure they feel like they are the best team, the Bulls feel like they are the best team, Oklahoma City feels like they are the best team.
"That is the way we are going to attack it."
Information from ESPNNewYork.com's Mike Mazzeo was used in this report.