Bill Belichick talks to Chris Berman, Randy Moss and Steve Young after the Patriots erase a 25-point deficit and rally past the Falcons in overtime to win Super Bowl LI. (3:30)

HOUSTON -- Tom Brady looked exhausted. Bill Belichick was subdued.

The greatest quarterback and perhaps the greatest coaching mind in NFL history had just engineered the most incredible victory for the New England Patriots, a 34-28 overtime win over the Atlanta Falcons in Super Bowl LI in which the Patriots rolled off 31 unanswered points. It was the greatest comeback in Super Bowl history and one of the greatest comebacks in league history.

Together, Brady and Belichick have won five Super Bowls in seven appearances and have been to 11 conference championship games. But the sight of them after the game fit their styles. Belichick looked like a coach and leader ready to roll up his sleeves and begin preparation for their next Super Bowl run. Brady looked like a quarterback ready to take a one- or two-week break and start working on next season.

Mentally, the work already appears to have started. Brady is starting to get word to the Patriots that he would like to play for at least three more seasons. Belichick is thinking about the Patriots' next run and has already started to shape his roster for the future.

Now it's time for New England to try to make a run for its sixth championship.

While odds might be against an immediate repeat trip to the Super Bowl next season, it's not out of the question. The Patriots are in a great spot to go 4-2 or 5-1 in the AFC East. The Buffalo Bills made a coaching change after a 7-9 season. The Miami Dolphins won 10 games on an easy schedule in which they beat only one team with record of .500 or better. Their schedule is tougher next year. The New York Jets dropped from 10 wins to five and will undergo a roster rebuild.

Linebacker Dont'a Hightower is a free agent after the season, but the Patriots could give him a long-term contract. Robert Deutsch-USA TODAY Sports

The reason I say Belichick began working on the next Super Bowl run in the past year is he made some bold moves to find starters. He traded Pro Bowl pass-rusher Chandler Jones to the Arizona Cardinals and got a 2016 second-round pick. The Patriots dropped down in the draft and ended up with guard Joe Thuney in the third round and wide receiver Malcolm Mitchell in the fourth.

Thuney started 16 games at guard. Mitchell caught 32 passes for 401 yards in the regular season, plus 70 yards on six catches in the Super Bowl, and looks like a steal. The Patriots have had some high-profile misses on wide receivers, but Mitchell looks like the real deal. Instead of waiting until 2018 and getting a third-round compensatory pick for linebacker Jamie Collins, who was expected to leave after the season, the Patriots got a 2017 third-round compensatory for Collins by trading him to the Cleveland Browns.

So Belichick planned ahead and picked up three draft choices over two drafts who could end up being starters.

Understand that Belichick has more experience than any front office decision-maker in NFL history in dealing with the aftermath of a Super Bowl run. In trying to keep a team together, success can be the enemy. Opponents want to land players from Super Bowl teams because they are winners, and the Patriots have been the standard of success.

All you have to do is listen to the immediate postgame response of tight end Martellus Bennett, who came to the Patriots in a trade before the 2016 season and is a free agent this offseason.

"I'm going into free agency as a Super Bowl champ," Bennett said. "You know they overpay Super Bowl championships."

Jones and Collins were Super Bowl champs two years ago. Collins signed a four-year, $50 million deal with the Browns last month. Jones is expected to get the franchise tag at $15.3 million in Arizona.

The Patriots have 14 unrestricted free agents and have some big decisions to make. Bennett could command between $7 million and $9 million a season on the open market. Cornerback Logan Ryan might get $8 million or $9 million a year. That's a problem for the Patriots because they also have to pay top cornerback Malcolm Butler, who's a restricted free agent who will likely get a deal worth $10 million to $12.5 million a season.

Tom Brady will be 40 when the 2017 season begins, but he expects to play for a few more years. Kevin C. Cox/Getty Images

Linebacker Dont'a Hightower might be the free agent who could get the biggest contract. He should get at least $12 million a season. The salary cap prevents teams from keeping every player, and no team knows that better than the Patriots.

"I guess it's up to me whether I will be on this team next year or not," Hightower said after the win. "Right now I'm going to enjoy tonight and celebrate this, take a few weeks to relax and then see what happens."

The Patriots will have a little more than $60 million of cap room after they re-sign practice squad players, but the money will go quickly. Butler should get some kind of deal. It's debatable whether they will keep Jabaal Sheard. LeGarrette Blount, Brandon Bolden, Alan Branch, James Develin, Duron Harmon, Chris Long, Barkevious Mingo, Greg Scruggs and Sebastian Vollmer are their other free agents.

Figuring the Patriots might lose four or five from this list, they will put themselves in position to get compensatory picks in 2018, hoping to get future starters or usable role players.

That means the Patriots might be a little younger and a little thinner at some positions. It could cause the Patriots to go from a 14-win team to a 12-win team, which still isn't bad. They will be in position to get a No. 1 or a No. 2 seed in 2017 and in the mix to represent the AFC in Super Bowl LII.

Belichick just has to develop a group ready to pounce on one or two more trips before Brady retires, and more young players are starting to emerge. Hightower, for example, said after the game that defensive end Trey Flowers is developing into one of the best defenders on the team. Belichick already sees rookie linebacker Elandon Roberts as a good enough player to fill part of the hole Collins' departure left. The trade for cornerback Eric Rowe gives the Patriots a cornerback to match up against bigger receivers, which is important in case Ryan leaves. Malcolm Brown is a good defensive tackle who's only 23. The interior offensive line is young. Running back James White has developed into a pass-catching halfback from the backfield, filling the Shane Vereen role.

So Brady and Belichick will savor this title for now, and then it's back to work on getting their sixth Super Bowl championship. That groundwork for their future has been laid for some time.