Russell's death on Sunday at age 88 had Belichick reflecting on that visit, and current Patriots players reflecting on Russell's legacy.
"It was great," Belichick said. "Bill's a great person. His comments on leadership, teamwork and unselfishness are all outstanding."
Belichick's close friendship with football great Jim Brown led to his connection with Russell, setting the stage for the 2001 visit. This week, the Patriots' two longest-tenured players -- Matthew Slater and Devin McCourty -- shared how Russell impacted their lives.
"It's really hard to put into words what Bill Russell meant not only to this city, but to professional sports, has meant to Black athletes, and just the progress we've seen in this country over the last 60 years or so," Slater said.
"When I think of Bill Russell, I don't think of, necessarily, the championships. Or the Celtics and the winning, which is a legacy that speaks for itself. I think of what he did for Black athletes. I'm a beneficiary of the actions of men and women like Bill Russell, who are willing to step out on the limb and advocate for Black athletes and Black Americans, and push for change, push for equality."
Slater was referencing, among other things, how Russell boycotted a 1961 exhibition game to protest discrimination.
For McCourty, who describes himself as a "huge basketball fan", playing professional football in New England drew him closer to Russell.
"Coming here, and just learning his story, initially all you know is 'Bill Russell, a champion, and winner.' But just his willingness and vulnerability to be very open about what he went through and wanting change," McCourty said.
"As an athlete that gets to play in this area, I drew a lot of inspiration and motivation from how he viewed things. I think the road he paved for Black athletes to be able to be successful in this city, and sports in general; I think about his life ... he wasn't just a great athlete, but he was a better person. All of us here, we strive to be like Bill Russell."
In an interview with Sirius XM NFL Radio, Belichick shared more detail on the time Russell visited the Patriots.
"He's a big Patriots fan and gave us a lot of support, and he was just a tremendous person to talk to. I've learned an awful lot from Bill Russell. Very fortunate to have had a relationship with him," Belichick said.
"Obviously he was a great player and there was a lot of attention on him, but how he tried to deflect that and enhance other players, how to help other players play better, what he could do to help his teammates.
"Ultimately his role changed from player to coach, to some combination of both, and so he talked a lot about how being a leader -- and how being a coach combined with being a player -- was really the ultimate in trying to help the team.
"And when you have veteran players on every team, which we had at that time and still have now; how those players are more than just good players, they're mentors, they're leaders. They have to find ways to help other players play better and still sustain their level of play. And that's what the great players do. And we've had a lot of them, but Bill really put it into a great perspective."