METAIRIE, La. (AP) — Sometimes criticized for a lack of patience as a play-caller, Sean Payton intends to take a far more methodical approach to the offseason.

After emerging from an exit meeting with his team on Monday, Payton pointedly refused to discuss possible changes on his coaching staff or roster that could help return the explosive but inconsistent New Orleans Saints to playoff form.

‘‘The day after the season ends, we’re not answering those questions,’’ Payton said. ‘‘It’s unfair to point out specific players or coaches.’’

Several teams around the NFL made major changes immediately, including the New York Jets, Cleveland Browns and Detroit Lions, who were already looking for new head coaches when Payton met with reporters at the Saints’ suburban New Orleans headquarters.

Payton said he was in no hurry to orchestrate a shake-up to pacify his or his team’s critics.

‘‘This is an important part of the year because this is where a mistake made can set you back or the right decision can set you forward, so we take it very seriously,’’ he said.

The Saints have failed to make the playoffs for two straight seasons, languishing in mediocrity with records of 7-9 in 2007 and 8-8 in 2008. Yet they have been competitive enough since Payton took over in 2006 that they shouldn’t require a major overhaul. Some aspects of New Orleans’ latest campaign were extraordinary. They accomplished things their fans had never seen in the franchise’s 42 seasons.

New Orleans set single-season franchise records for scoring (461) and yards (6,571), leading the NFL in both categories. Drew Brees came within 16 yards passing of breaking Dan Marino’s 1984 single-season record of 5,084 and only the second quarterback ever to eclipse 5,000 yards.

That the Saints could be so prolific even while Reggie Bush, Jeremy Shockey and Marques Colston all missed no fewer than four games each with injuries should be a scary thought to defensive coordinators who have to face New Orleans next season.

Shockey said his season was a disappointment and that he would participate in the Saints’ offseason program in New Orleans rather than working out on his own, something he never did with the New York Giants.

‘‘I was planning on being on a team going deep in the playoffs and putting up a lot more numbers than I have individually,’’ said Shockey, who had 50 catches for 483 yards and no touchdowns. ‘‘Next year, I’m excited about helping this team win, excited about getting healthy and actually showing the fans and teammates how effective I can be when I’m 100 percent.’’

If the Saints had a shortcoming on offense, it was the running game, which ranked 28th in the league. It was a liability in several close losses that came down to untimely failures in short-yardage situations. While the Louisiana Superdome crowd often urged Payton to run Deuce McAllister, the coach resisted at times, saying McAllister’s knees were bothering him more than McAllister himself was willing to let on. By contrast, the coach routinely touted the emergence of second-year running back Pierre Thomas, who ended up leading the team in rushing (625 yards), flourished on screen passes and finished with 12 touchdowns.

Lacking his old speed, McAllister’s longest gain was 20 yards on a swing pass. But his vision and power remained evident as he averaged about 4 yards per carry. Although Payton said it was premature to say whether the Saints will try to keep McAllister next season, the popular running back has acknowledged he may not be back.

‘‘I haven’t played as much as I wanted to,’’ said McAllister, who would be due about $7.2 million next season if the Saints didn’t release him or restructure his contract. ‘‘I want to be a part of this team. I want to be a part that is able to play and contribute.’’

McAllister said it would mean ‘‘a lot to be able to finish here in New Orleans … but at the end of the day, obviously, economics will come into play.’’

On defense, the Saints ranked in the bottom third of the league in yards allowed per game (339.5) and points allowed per game (24.6). They were beset by injuries to key players, including starting cornerbacks Tracy Porter and Mike McKenzie and defensive end Charles Grant.

Still, Jonathan Vilma improved the play of the linebacker corps. His 132 combined tackles and assisted tackles ranked ninth in the NFL. He also had a sack and an interception. Meanwhile, rookie defensive tackle Sedrick Ellis improved the interior defensive line.

Payton said it’s obvious the defense needs to improve, but he defended defensive coordinator Gary Gibbs, who has been with the Saints since Payton took over three seasons ago.

Gibbs and fellow defensive assistants have ‘‘done a real good job of fighting through the injuries and some of the adversity they’ve had and when you lose your two starting corners, you lose a starting defensive end in Charles Grant, Sedrick Ellis is out for four weeks,’’ Payton said. ‘‘You go on and on. That’s the hand we were dealt.’’

The Saints could certainly use the addition of a high-profile free-agent in the defensive backfield, but they also have to worry about retaining some of their own players who had strong seasons. Vilma will be a free agent, but he has said he’d prefer to return to New Orleans. On offense, right tackle Jon Stinchcomb will be a free agent, while guard Jahri Evans and receiver Lance Moore will be restricted free agents.

Thomas, initially signed as an undrafted free agent, is under contract for another season, but the Saints may want to sign him to a more lucrative extension, given he was the team’s top rusher.

‘‘It would be easy to say with where we finished offensively we’re going to point to defense,’’ Payton said. ‘‘Some of that might be true, but nonetheless we have to pay close attention to our own players offensively that are free agents right now. There are a few of them that were big contributors to what we did this year.’’ 1/4