Dave is right, I was writing as an explanation for the noise but artistically, if anything the image is slightly over exposed because the frame is lighter than the scene was if a silhouette was desired. It is not a bad photo underexposed, it is correct to be underexposed.
One thing to keep in mind, what the light meter in the camera is tell us. It sees the world differently than we do, it expects the mid tones to be 18% of the way between the blackest black possible and the lightest light possible. Our eyes and brain combine to perceive the mid point between the whitest white and the blackest black when there is 18% mix of light. The camera wants every scene to be centered on that mid point of perceived illumination. We know of course, that many scenes are not centered around that 18% level, where the subject is brighter than middle middle grey, and other sense look natural when darker. This is the reason we get dull grey snow in winter landscapes and dark grey wedding men's suit coat that in life is very dark, not grey. With a little experience, we can judge the difference between what the camera thinks is right and what human viewers think it correct and adjust the camera accordingly. The snow scene looks correct to us if we dial in positive exposure compensation, around 2 full stops, to purposely over expose the shot(over exposed from the camera's opinion) and we dial in negative compensation to turn the image of the man's tux black as our eyes see it. The increase or decrease in exposure compensation impacts the noise so that becomes part of the judgement call we make. Shooting night scenes is often done by leaving it to the camera but that results in more illumination that actually is seen by our eyes so it is not very natural looking or quiet or free from noise. The camera sees the scene as needing to be brought up to daylight brightness, or a dull overcast day's brightness if allowed to control the exposure completely, resulting in a lot of additional noise from the increased exposure amplification. It appears that many people think low light performance relates to having dark scenes having the same color, detail and brightness as a daylight scene, which is what I call the nightscope syndrome. To our eyes, dark scenes really do have less color and detail information and it is unnatural looking to appear otherwise. The reasonable use of high ISO performance is to increase shutter speeds for unblurred action, not turning dark scenes bright.
Pixel peeping is the enemy of peace of mind for photographers. You will never be happy if you view your, or anyone's images at microscopic scales. Camera, printers and screens are intended to produce images looking correctly when viewed at normal viewing distances and sizes, human scales. The exact complain of too much noise exists for people who do their viewing of a master's painting from 2 inches away with an 10X inspection loupe. Such microscopic inspection only makes sense when using that scale of observation to authenticate a painting looking for artifacts that might reveal the actual painter. Looking in that way can produce information that is useful but tells nothing of the quality of the work or meaning. Same with photography. Pixel peeping tells nothing of the quality or meaning of a photograph but can be used for specific diagnostics such as looking for artifacts of processing or focus mechanism. Expecting to determine qualitative merit of the photo is not what zooming in is for or useful for.