Violent scenes need the same treatment as any other scene. You wouldn't focus all your attention on your character's action while she's out jogging with a friend:
Holly put one foot in front of the other while her arms pumped at her side. She reached around to scratch an itch on her back. A tiny pebble trapped in her shoe dug into her big toe.
A violent scene can also suffer with too much focus on action:
Fiona felt a hand on her shoulder, then a sharp pain in her legs as they were swiped out from under her. Her face was pressed to the concrete, a knee or an elbow jammed into her lower back, pinning her down.
While something is happening to the physical body, the other facets of the human experience—emotions, fears, desires—are absent.
In Russell Banks' novel The Sweet Hereafter, a school bus accident kills most of the town's children. In the first chapter, Dolores, the school bus driver, documents the events of the morning of the accident. She describes all the stops she made and lingers on the “red-brown blur" that she swerved to miss, thinking it was an animal or a child:
For the rest of my life I will remember that red-brown blur, like a stain of dried blood, standing against the road with a thin screen of blown snow suspended between it and me, the full weight of the vehicle and the thirty-four children in it bearing down on me like a wall of water. And I will remember the formal clarity of my mind, beyond thinking or choosing now, for I had made my choice, as I wrenched the steering wheel to the right and slapped my foot against the brake pedal, and I wasn't the driver anymore, so I hunched my shoulders and ducked my head, as if the bus were a huge wave about to break over me. There [were] . . . the children of my town—their wide-eyed faces and fragile bodies swirling and tumbling in a tangled mass as the bus went over and the sky tipped and veered away and the ground lurched brutally forward.
The character's state of mind is important in all scenes, including those that have intense action. In Nelson Algren's The Man With the Golden Arm, Frankie Machine, a card dealer and a junkie, is running away from the police. A bullet hits him as he flees: “a brief, cold, painless flame, like the needle's familiar touch, brushed his heel." It's not until later, when Frankie is on the El that he realizes he's been shot:
But it was hard, with the breath hardly back in his lungs, to ease himself far. He counted three stations: they had just passed Franklin and Wells when the sweat in his socks began stinging and he looked down.
He was on his way all right. With a sockful of blood.
You'll need to address action, but don't let it take over. In fiction, physical action gains emotional heft and meaning when filtered through your character's experience of it.