Should I be worried about the pixelation in my photo?
Not in this case, because what you are describing is noise. That is a totally diferent issue than pixelation.
Pixelation is when you rescale an image too much that the individual pixels shows.
Should I be worried about noise in my photo?
As you said, noise is most apparent in low light scenarios. Period. Actually, all images have noise, but you see it more clearly on the dark part of the photo.
This dark part of the photo can be on any photo, but on a dark scene, normally you need to blow the dark zones so the noise is visible.
Shooting in raw gives you a little more freedom to control it. You can also apply some filters to reduce it.