A smaller aperture does increase depth of field, but it doesn’t guarantee a sharper photo overall.

On a camera like the FinePix HS10, stopping down too far can introduce diffraction, which reduces fine detail and makes the image look softer. With small-sensor cameras, diffraction can become noticeable relatively early, so f/11 may be beyond the sharpest range. In practice, f/4 to f/5.6 may give better overall sharpness on your camera.

There’s also a second possible cause: at f/11 less light reaches the sensor, so the camera may use a slower shutter speed and/or higher ISO. A slower shutter can cause camera shake if handheld, and moving leaves or branches can blur from wind during the exposure.

So the softness at f/11 is likely a combination of diffraction and possibly motion blur. For landscapes, try using the sharpest middle apertures on your camera (often around f/4–f/5.6 on small-sensor models), keep shutter speed high enough, and use a tripod if light is low.