FOXBOROUGH, Mass. — Bill Belichick can add another division championship hat and T-shirt to those overflowing reminders of his accomplishments.

But it’s the Super Bowl clothing — and trophy– that the coach of the New England Patriots and his players really want. And winning the AFC East the past two seasons didn’t keep them from losing their opening playoff game each year, both at home.

So forget about the garb the Patriots earned Sunday when they won the division title for the ninth time in 11 years with a 41-23 victory over the Denver Broncos.

“Unfortunately, after 36 years of coaching I’ve accumulated a lot of stuff. Way too much. Game plans, T-shirts, programs. You name it,” Belichick said Monday. “It’s hard for me to take something that you’ve worked that hard on for a long period of time and is that important to you — even though it was only one week of your life … to just put that in the trash can and say, ‘I don’t care about that anymore.’ “

This week, Belichick will work hard preparing for Saturday’s home game against the Miami Dolphins. Then he’ll focus on the final regular-season game, on New Year’s Day against the Buffalo Bills, also at home.

“I mean, wow! AFC East champs,” safety James Ihedigbo said. “We have a competitive division, a lot of great teams, and to work as hard as we have this year and come out on top, it’s a big step in the right direction. We have a few more championships to win, though.”

Like his new teammates, Ihedigbo also fell short the past two years when he was with the New York Jets. They made it to the AFC championship game both times — eliminating the Patriots along the way, 28-21, last season — but lost to Indianapolis and then Pittsburgh.

On Sunday, the Patriots fell behind 16-7 as the Broncos scored on their first three possessions. Then the Patriots made defensive adjustments, controlled Tim Tebow and the running game and outscored Denver 34-7 after that.

“We were determined,” Ihedigbo said. “It was tough early, but we focused and settled down and played great ball the rest of the game. And now I’m wearing one of these (championship) hats.”

What made the victory more impressive was that the Patriots sustained another key loss on defense when Andre Carter injured his left quadriceps late in the first quarter. Carter, who leads the team with 10 sacks, could miss the rest of the season. Two other starters were sidelined for the sixth straight game — safety Patrick Chung with a foot injury and linebacker Brandon Spikes with a knee injury.

“That’s tough. Andre puts so much in with his leadership alone,” defensive tackle Vince Wilfork said. “He hasn’t really won a lot in his career (five years each with San Francisco and Washington), but now he’s winning, he’s happy here, he’s having fun, he’s playing well. To see him go down, it’s a blow.”

Even with Carter, the Patriots have allowed the most yards in the NFL this season. Still, they own the AFC’s best record at 11-3.

They switched this year primarily to a 4-3 defense, in part because Carter performs best at defensive end. Without him, they could revert to the 3-4, especially if Spikes returns and can line up next to Jerod Mayo at inside linebacker.

“I think you can get into a lot of technical aspects of defense and strategy and all that, but we played plenty of four-man line, we played plenty of three-man line,” Belichick said. “We used them both at different times for different reasons. In the end, it comes back to the players — beating blocks, making tackles, hitting the quarterback, covering the receivers.”

After the first quarter Sunday, they did an outstanding job.

And with the offensive production of the Patriots, the Broncos were too far behind for Tebow to lead another fourth-quarter comeback.

“We approached this game just like any other,” Wilfork said. “We’ve faced some decent quarterbacks this season. Tebow does some things that most quarterbacks don’t do, but this is the National Football League. There’s going to be a point in the game where you have to make sideline adjustments, which we did.”

On offense, the Patriots had another outstanding performance at tight end.

But this one came from Aaron Hernandez, not Rob Gronkowski.

Hernandez led the Patriots with nine catches for 129 yards and a touchdown and even lined up in the backfield and ran once for 16 years. Going into the game, it was Gronkowski who had overpowered defenses with 71 catches, 15 scoring receptions and one rushing touchdown.

But the Denver defense double-teamed Gronkowski at times, making it easier for other receivers.

“You never know who is going to be heavily involved,” Gronkowski said. “That’s what is so great about the game. It takes a team effort every single week. You don’t know who is going to be the guy getting the ball every single week. It happened to be him this week. He played great. He juked a lot of guys, got a lot of extra yards. I loved watching him do that kind of stuff, so it’s cool.”