Some might complain that “9/11” reduces the events of September 11, 2001, to just another disaster movie, but that’s actually one of its strengths: this isn’t a film that tries to parse the big, awful picture of what happened that day, or the geopolitics that led to it or the worldwide reverberations it caused. By focusing on a small group of people trapped somewhere they shouldn’t be, the film can, at least intermittently, succeed as a human-sized drama.

In fact, titling the movie “Elevator” — the name of Patrick Carson’s original play, adapted here by Steven James Golebiowski and director Martin Guigui — might have relieved the film’s implied burden of telling such an immense story, even if its nomenclature would have been much less marketable. It’s a flawed production that can barely hide its low budget or its theatrical roots, but it never becomes the tacky exploitation exercise that you might expect from a movie called “9/11.”

If nothing else, the writers pass the major hurdle required of all historical dramas; the story generates suspense even though we already know the larger outcome. The five people in the elevator are in no way meant to stand in for every single casualty that day — and how could they? — but as they provide a glimpse into what it must have been like to be trapped in one of the Twin Towers, I genuinely cared about whether or not they would make it out alive.

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The characters come together briskly: World Trade Center building supervisor Metzie (Whoopi Goldberg) pops by a diner on her way to work, where custodian Eddie (Luis Guzmán) has his coffee break interrupted with an assignment to unclog a toilet on one of the upper floors. Bike messenger Michael (Wood Harris, “Creed”) tries to get through errands so he can make it his daughter’s birthday. An upset Tina (Olga Fonda, “The Vampire Diaries”) has personal business to attend to, and billionaire Jeffrey (Charlie Sheen) and his wife Eve (Gina Gershon) hammer out the final details of their divorce, which she wants more than he does.

As Metzie runs the control board downstairs, the other five are riding in an elevator when the first plane hits, trapping them. As they try to make their way out, with Metzie providing guidance from the ground floor, they unburden their feelings and anxieties with each other. (Michael, clearly having seen this kind of movie before, says, “I’m not doing this” when it comes his turn to share with the group.) More effective than the chat are the escape efforts, which offer genuine suspense.

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It’s the ensemble that makes this material work more often than it doesn’t; Sheen lacks the vitality he once brought to the screen, but neither does he embarrass himself. Harris, Goldberg (saddled with an unfortunate wig) and Guzmán are solidly empathetic and relatable in unshowy character turns.

It’s Gershon who really shines here. Her telephone scene with Jacqueline Bisset, as her mother, carries the power and the tragedy of those real-life calls we heard that day from the World Trade Center; that moment, and a later exchange between Bisset and Prestyn Bates as Jeffrey and Eve’s son, go a long way toward giving “9/11” the dramatic impact it needs.

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On the minus side, there’s Fonda, who wears Tina’s insecurities on both sleeves, and the muddy cinematography by Massimo Zeri, which gives the film the copy-of-a-copy look you’d expect from a bootleg DVD you bought in Times Square. Jeff Toyne’s score comes within about four bars of overdoing the angelic choir, but it’s mostly effective.

Sixteen years later, 9/11 remains too touchy a subject for a movie as clumsy as “9/11” to get entirely right. And even if the film relies too much on the real-life horror of the actual event to loan it some gravitas, the performances touch the emotions honestly and deservedly.