On April 2 last year, New York band LCD Soundsystem played their last-ever gig – a four-hour, 29-song set at Madison Square Garden.

Frontman James Murphy wore his trademark black suit as he prowled the stage performing songs like Losing My Edge and North American Scum. The rest of the band dressed in white, as did most of the 18,000-strong audience. At the encore, with some in the crowd in tears, the famous arena was swamped by thousands of white balloons falling from the ceiling.

The news that the 42-year-old was calling time on LCD Soundsystem's ten-year, three-album career had come some months earlier in an announcement placed on the band's website. "We are retiring from the game, gettin' out, movin' on," it read. If the last show was to be a funeral, it added, "let's have the best funeral ever".

Most funerals aren't attended by documentary filmmakers commanding a 13-camera set-up, but this one was and here's why. LCD Soundsystem may have only rarely troubled the pop charts – only six of their 18 singles even charted in the UK and only one made it into the top 30 – but their albums are critically acclaimed in all the right places and, since their 2002 debut, their sassy, spikily literate songs have won them a dedicated fanbase among the sort of people who know their Can from their Tin Machine. They made clever, reflective, self-referential music which commented on its own influences – dance music and punk rock primarily – while creating something new out of a synthesis of those two forms.

In a world where most bands don't matter, they do. Fittingly, then, the "funeral" was recorded and filmed. The result is Shut Up And Play The Hits, part concert movie, part quirky documentary.

Directed by Will Lovelace and Dylan Southern, the British pair responsible for Blur documentary No Distance Left To Run, it follows Murphy in the lead-up to the final concert, on the night itself and on the day after.

It features 11 songs interspersed with shots of a bleary-eyed Murphy taking his dog for a walk in his pyjamas, making coffee in the empty office of the record label he runs, trimming his stubble, and picking over the bones of the night before with the band's manager, Keith Wood. The title comes from the words shouted over the mic during the concert by one of the band's guest backing singers, Arcade Fire's Win Butler.

"We didn't want a behind-the-scenes rockumentary thing," Murphy explains when I ask him about the origins of the film and its unusual format. "At one point we talked about doing a completely fictional movie, and that was exciting to us. But while we were talking about that, I said 'Oh, I'm going to end the band and we should get one shot from Madison Square Garden for this movie that's going to have no music in it'."

As it turned out, getting that one shot would have incurred an "insane fee", so Murphy and the filmmakers decided to shoot the whole concert. That necessarily meant a film with lots of music in it.

"Initially we weren't considering filming the show, though in retrospect, I feel like an idiot," Murphy says. "If I hadn't filmed it, it would have been absurd. Then I would have had to have dealt with people's iPhone footage of it on YouTube. So it then took over. We said 'Why don't we make the film about the end of the band?' It seemed to be the right thing to do."

The film also shows Murphy being interviewed – briefly, on television, by high-energy chat show host Stephen Colbert, and at length in a deserted restaurant by cultural commentator and music critic Chuck Klosterman.

"You're walking away from fame," says Colbert in the clip. "Why?"

"I really like making coffee," Murphy quips in reply, looking not at all at ease as he perches on a stool in the studio. If ever you wanted an example of the accidental rock star, this is it.

Murphy isn't slow to admit it. "For a guy who grew up feasting on things like glam rock, it's something I've always been a little bit shy about, so I admire people who do it well," he tells me. "Kanye West does it well. He makes the world more interesting in a fundamental way and it's just unapologetically him. I'm not programmed to do it."

But away from the concert footage, it's the interview with Klosterman which acts as the film's spine as the pair discuss everything from Thomas Pynchon to David Bowie. The two men know each other of old and they're a good fit.

In a 2010 interview for a British newspaper, Klosterman wrote that what Murphy and LCD Soundsystem do in almost every song is "dissect and reconfigure" coolness and what it signifies. That could also be a statement of Klosterman's areas of interest. He's at his best when explaining why bands matter to fans and when examining both the absurdities of rock-star fame and fandom itself. He's also very, very funny.

"I didn't want to talk to the camera, I didn't want to talk to filmmakers pretending that we hadn't talked before, and I didn't want narration," says Murphy.

"One of the interviews I remember most fondly was one Chuck did with me so I said: 'Let's just ask him to do it'. So we invited him over to eat in this restaurant and gave him four hours.

"I feel like Chuck's savvy enough to puncture holes in mythologies but doesn't do that to want to destroy something. If everyone's fawning over something, he won't find fault with it to be bitter, he'll just say I don't really think that's what's happening."

Film being film, there's a level of artifice at play too. The opening scene in which Murphy wakes with a hangover in his light-filled Brooklyn apartment on the morning after the farewell gig is a case in point: he'd given keys to the camera crew so they could let themselves in, he says, and was perfectly aware that they were filming him.

But Southern and Lovelace capture the naked emotion of the day as well. When Murphy travels to the lock-up where the band keeps its equipment – gear that is to be sold off now that LCD Soundsystem is no more – he's overcome and sobs quietly as the camera keeps a respectful distance.

"It was sad," he laughs. "It was like a graveyard. What you don't see is that on the other side of the room there was even more stuff. That was the small pile."

Ironically, the fact of making a film about the death of LCD Soundsystem has prolonged its life. A year and a half on, Murphy is still talking about the band, and his work on the film continued long after the last of the white balloons had been popped, as he mixed the sound from the concert scenes.

"Another year of work was not what I was planning but luckily I get along with the filmmakers and it was fun," he says. "But I was like: 'Holy crap, did this thing die? Can I get on with my life?'."

But looking at the footage of that epic final concert, reliving the memory of performing at the famous New York venue – and perhaps even thinking back to Stephen Colbert's apparent incredulity that a rock star would down tools like this – does he feel regretful about ending the band, or vindicated in his decision to talk away?

"I don't know that I can feel vindicated because I wasn't trying to make a point, I was making a decision for my life more than anything," he says.

Besides, he adds, "all the people in the band are still in my life - For the most part I overburdended them with it. These are really good friends of mine who never intended to be in a band like this."

And perhaps it's that fact alone which has made LCD Soundsystem's passing so remarkable: they were the accidental rock stars who never wanted any of it. Don't hold your breath for a 2020 reunion tour, then.

Shut Up And Play The Hits is in cinemas nationwide for one night only on Tuesday, followed by a live Q&A feed with James Murphy. For additional cinema dates at local venues, see

www.shutupandplaythehits.com. The

film is released on DVD on October 8