EAST RUTHERFORD, N.J. - Rex Ryan fell just short in what could be his last home game as coach of the New York Jets.Nick Folks potential go-ahead 52-yard field goal attempt was blocked by Vince Wilfork, and the New England Patriots slipped past the Jets for a 17-16 win Sunday.Ryans future with the team is uncertain in his sixth season. New York will miss the playoffs for the fourth straight year, and Ryan and general manager John Idzik have come under heavy criticism by fans who have urged owner Woody Johnson to make changes.This was another game that I thought we had a heck of a chance to win against New England, Ryan said. Thats been the story probably the last four out of five times we played them.Several fans waved yellow penalty towels at MetLife Stadium with the words Fire Idzik! printed in green. This latest loss certainly didnt make the Jets faithful — or Ryan and Idzik — feel any better about their situation.Today being our last home game of the season, obviously we wanted to leave our fans with a good taste in their mouths and go out on a good note, Jets quarterback Geno Smith said.But we fell short today and I feel bad. I feel terrible. When you put your heart out there, when you play as hard as you can, you want to come away with a victory and be fulfilled.The Jets (3-12) finish the season next week at Miami.The Patriots (12-3) earned a first-round bye and could clinch home-field advantage throughout the AFC playoffs if Cincinnati beats Denver on Monday night.Marcus Williams first NFL interception put the Jets in position to go ahead when Tom Bradys pass tipped off Brandon LaFell and into his hands. But Donta Hightower sacked Smith on third-and-4 for a 10-yard loss, setting up Folks long attempt.Thats something you learn from, Ryan said. You cant take a sack there no matter who is in your face. Get rid of the football.After Folks miss, Brady and the Patriots were then able to run out the clock for the win, sealed by Brandon Boldens 17-yard run on third down with just under 2 minutes left.(There were) a lot of key plays at the end, Patriots coach Bill Belichick said. Our players came through on one right after the other.Brady finished 23 of 35 for 182 yards, a modest showing while playing without wide receiver Julian Edelman (concussion) and running back LeGarrette Blount (shoulder).Jonas Gray scored the go-ahead touchdown on a 1-yard run early in the fourth quarter after New England intercepted Smith.The Jets quarterback was 17 for 27 for 210 yards with a 20-yard touchdown pass to Jeff Cumberland. But with the Jets leading 13-10 late in the third quarter, Smiths pass for Jace Amaro hung in the air for an easy interception by Jamie Collins.Gray squeaked into the end zone up the middle — a video review stood after Ryan insisted on the sideline that the running backs knee might have been down — to give the Patriots a 17-13 lead with 13:51 remaining.The Jets then got into Patriots territory but stalled in the red zone — a common problem this season. They had to settle for a 37-yarder by Folk with 7:53 left that made it a one-point deficit at 17-16.Notes: Patriots CB Darrelle Revis had a mostly quiet return to the Meadowlands, playing against his former team for the first time since signing with New England — except for the fans booing him when he made a tackle. ... Jets C Nick Mangold injured his left ankle in the second quarter and was carted off the field. ... 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