After the Nets meekly bowed out of the playoffs following a disappointing first-round sweep by the Celtics, Kevin Durant acknowledged this offseason is going to be a pivotal one for the organization and its championship window.

And despite Kyrie Irving’s tone-deaf comments that he, Durant, owner Joe Tsai and general manager Sean Marks are part of a “co-management relationship,” rest assured Tsai and Marks — and likely Durant as well — will have some big decisions to make in the coming months.

“This summer is going to be a very, very important summer for our organization,” Durant said. “We’ll see where we go next year.”

The Nets must go further than another first-round exit. If they don’t, there will almost certainly be a massive overhaul, with heads rolling, not just the tinkering and fine-tuning expected this summer.

But there are plenty of pivotal decisions to be made. And both Irving and head coach Steve Nash figure to be at the heart of them.

Will Nash be back as coach?

All signs point to the answer being yes.

Granted, it was conspicuous that Irving spoke of “managing this franchise” alongside Durant, Tsai and Marks, with no mention of Nash.

Nash — who in fairness made a number of adjustments, from trying Durant on the elbow in screens to 1-2-2 zones — has private backing in the organization and public support from Durant, who said Nash is still the right man for the job.

“Yeah. Steve’s been dealt a crazy hand the last two years,” Durant said. “He’s had to deal with so much stuff as a head coach, a first-time coach: trades, injuries, COVID.”

Might Nash’s staff look different? During the 2020-21 season, the Nets had Mike D’Antoni coach the offense and Ime Udoka the defense. Both were sorely missed this season.

Now, Nets consultant Steve Clifford has been given permission to interview for the Kings position (up against D’Antoni). If the Nets don’t replace Nash, they may need to help him.

Speaking of Irving, how will his contract end up?

There are a multitude of ways this can play out.

Irving has a $36.9 million player option that he seems likely to decline, but that doesn’t mean he will be leaving in free agency.

Tsai tabled a max extension for Irving last summer, and those talks were only put on hold because of Irving’s unexpected refusal to adhere to New York’s COVID-19 vaccine mandates, a decision that cost him two-thirds of the season.

Irving can re-sign for five years and $247.6 million. If he opts out, he can extend for four years, $191.3 million, according to HoopsHype. That would line his deal up with Durant’s, through the 2025-26 season.

Of course, the nuclear option would be Irving — whose part-time status contributed to James Harden’s trade demand, which sent him to the rival 76ers — signing elsewhere for four years, $183.6 million. The Nets are over the cap and would be unable to replace him. But that’s unlikely.

“I don’t really plan on going anywhere. This is added motivation for our franchise to be at the top of the league for the next few years,” Irving said. “I’m just looking forward to the summer, and just building with our guys here.”

ESPN suggested those summer conversations will center around the length of the deal. Irving’s unpredictable nature would make protections wise.

What’s wrong with Ben Simmons, and can the Nets get him right?

With Simmons under contract for three more years, the Nets are committed. But is he?

The 25-year-old has drawn arched eyebrows from some within the Nets organization for everything from his flashy attire courtside while not playing to his abrupt about-face in not playing Game 4 against Boston.

While Simmons’ back improved in recent weeks and a source told The Post he’s expected to avoid surgery, now it appears the issues keeping him off the court are more mental than physical. But considering he cost them Harden, a former MVP, it’s paramount this gets sorted out and reset over the summer.

“Ben’s good, we have Ben, we have his back, he’s going to be good for next year,” Irving said. “Now we just turn the page and look forward to what we’re building as a franchise and really get tougher.”

What are the building blocks for that?

The Nets aren’t going to have 10 new faces as they did this past offseason, but they do have a host players who will be free agents, not including Irving.

LaMarcus Aldridge, Bruce Brown, Nic Claxton (restricted), Goran Dragic, Andre Drummond, David Duke Jr. and Blake Griffin will be free agents, and Patty Mills (like Irving) can opt out.

Griffin and Aldridge (who’s 37 and did not appear in the playoffs) appear unlikely to return.

Former Nets GM Bobby Marks — now an ESPN front-office insider — told The Post that the taxpayer mid-level exception should be more than enough to retain Drummond. But is that even the best use, with the Nets desperate need of a long, defensive wing?

Claxton could inherit the center spot, regardless of whether Drummond returns. Forget his 1-for-11 performance Monday from the free-throw line, his ability to switch on defense, athleticism and length make him a priority. Claxton can avoid restricted free agency altogether and extend by June 30 for up to four years and $55.6 million according to HoopsHype.

“I’ve done what I’ve had to do to put myself in position to be in a good spot,” Claxton said. “Hopefully it’s here, but we’ll see.”

At the break, Mills seemed sure to decline his $6.2 million option and get a raise, but overuse and fatigue led to a poor second half. The Nets have his non-Bird rights and can re-sign him for four years, $31.6 million according to HoopsHype.

Brown is an unrestricted free agent after having to play last year on the $4.7 million qualifying offer. After a strong second half, a league source said Brown could conceivably earn $14 million. He has said he wants to stay with the Nets, and they have his Bird rights.

“Yeah, hopefully,” Brown said. “If there’s a chance to stay then we’ll talk about it. But we’ll see.”

But with Simmons presumably stepping into the lineup and the Nets looking to add size, how would Brown fit in?

The Nets are flawed. How can they get better?

They needed more wing length to contend with the Celtics. Simmons and Joe Harris should help toward that end, but both are hurt and more is needed.

Retaining Drummond on another minimum or letting him walk (to spare the MLE) is one. That might be the path of least resistance to adding such a player.

Marks has 2022 and 2027 picks, acquired from the 76ers in the Harden swap, and seems likely to dangle them. (The 2022 pick can be punted to next year, when the draft is expected to be deeper.) The Nets also have five trade exceptions, the largest of which are $11.3 million and $6.3 million.

As Durant said, it’s liable to be a big summer.