Yes, if the DOF was larger, there would be more in focus.
I don't know how manual your camera will go, but generally, the larger the aperture the smaller the DOF.
So, what you want to do is to close down the aperture - this will likely lead to a longer exposure time.
Ultimately, the DOF is dependant on your lens, so you're stuck with whatever your camera can do.
FWIW, I quite like a tight DOF. Most of my stuff is shot with the aperture wide open.
On my 45mm lens, it's just crazy. I took it out to a birthday dinner thinking it'd be good discipline to just use one lens for the evening. Because the light was so low, I had to open the lens right up, which of course meant the DOF was really narrow.
Made composing the shot more challenging than if I'd been on my 28mm or 50mm. The 45mm just seems less forgiving. Good practice though.
