But to the Patriots, yesterday’s regular-season finale against Miami was not without value. Sure, there were some key players with injury issues who got the day off, but for the most part, it was all hands on deck.

And the result, a 38-7 dismantling of their AFC East foe, served as proof that the Patriots had no intention of treating Week 17 as a time to lay off the gas.

“We definitely had something to play for,’’ safety James Sanders said. “We wanted to continue to be playing good ball this time of year and we didn’t want to have any letup. We wanted to go out there and play solid football for 60 minutes and just continue to improve as a team, and that’s what we did.’’

Already eliminated from the playoffs and now facing questions on whether coach Tony Sparano will return for a fourth season and whether Chad Henne should be the team’s starting quarterback, Miami had little to salvage but its pride — and it didn’t put up much of a fight for that.

Henne was picked off on the Dolphins’ first possession of the game, Devin McCourty wresting the ball from receiver Brandon Marshall on a third-and-long pass. It was the seventh interception of the season for the rookie, and gave Tom Brady and the offense the ball inside of midfield.

“It’s a great spark any time you get a turnover like that on the first drive of the game,’’ Brady said. “We’ve been getting great field position from our defense this season, so it was good.’’

Once the Patriots’ offense took the field, it began racking up the yards and didn’t stop, finishing the game with a 2-to-1 advantage over its visitors: New England totaled 502 yards, while the Dolphins had just 250.

Forty-seven came after the McCourty turnover, with Danny Woodhead gaining 19 off a direct snap; Rob Gronkowski got the touchdown, making a hard cut on safety Chris Clemons into the end zone. Clemons couldn’t recover and Gronkowski pulled in his 10th touchdown of the season, from 13 yards out, setting team records for scores in a season by a tight end and most touchdown receptions by a rookie.

New England played without Deion Branch, Wes Welker, and Aaron Hernandez, all of whom were given the afternoon off for various reasons. In their stead, rookie Taylor Price saw his first action of the regular season, and Julian Edelman and Brandon Tate played larger roles.

Each had their moments, but Gronkowski was a standout. His six catches all went for a score or a first down, and he totaled 102 yards, the first 100-yard day of his nascent career.

The unassuming University of Arizona product, who has as much fun as any Patriot during games and during the week, felt he was just doing his job.

“[Branch and Welker] are out of the game for good reason; they’re great guys, obviously,’’ he said. “I had to step up, other guys had to step up, and we did. We had a great game overall.’’

There was but one negative moment offensively for New England, and it came on its second possession. On second down, Woodhead got the ball and it was knocked loose when he was hit by Kendall Langford. Paul Soliai recovered, marking the first time since the loss Nov. 7 in Cleveland that a Patriot had committed a turnover.

Woodhead suffered a concussion on the play and did not return.

But emblematic of its disappointing season, Miami could do nothing with the turnover, despite taking over just 34 yards from the end zone. After gaining just 12 yards, Dan Carpenter lined up for a 40-yard field goal and pushed it wide left.

A fake end-around to Edelman and a swing pass to the converted college quarterback that he took for 40 yards set up the Patriots’ second touchdown, a 1-yard run by BenJarvus Green-Ellis with 4:12 left in the first, and the rout was on.

The Patriots went into halftime with a generous 24-0 cushion thanks to Edelman, who returned a punt 94 yards for a score. Edelman thought he had a return touchdown in Chicago but it was taken off the board after a penalty.

Yesterday, after initially bumping into McCourty early in the return, Edelman found a clear path to his right and outran the Dolphins.

Ever prepared, Edelman and the Patriots believed they’d have a chance for a big return because Miami’s Brandon Fields is prone to outkick his coverage.

As he did last year, coach Bill Belichick threw Brian Hoyer a bit of a curveball, having him enter the game midway through a second-quarter drive, as could happen were Brady to get injured. But after four snaps and with the Patriots facing third down, Brady came back in the game.

Brady finished the second quarter and played the Patriots’ first series of the second half. He finished 10 for 16 for 199 yards and two touchdowns, extending his streak of pass attempts since his last interception to 335.

Hoyer took over with 10 minutes to play in the quarter and finished the game, getting his first NFL touchdown pass on a pretty 42-yard throw to Tate, who caught up to the ball and stretched out for the score.

Belichick was happy to see players who previously had gotten little playing time take advantage of the opportunities they were given, but he quickly turned the page to playoff mode after the game.

“Overall it was a pretty solid effort,’’ he said. “It’s good to end the season on this note, but right now we’re like everybody else — everybody is 0-0 at this point in the playoffs, so it’s time for us to get focused on the next target.

“I’m proud of the way the guys played. They stepped up and played like the AFC [East] champions that they are.’’