You can take pleasing night shots with compact digital cameras, only are you somewhat more limited, since often their smallest f-stop is f8 only and no smaller (applies to my Powershot), and you cannot expose for any longer than 15 seconds.
Those two things in mind, you can still have your camera give you nice photos at night, given you don't let the camera decide on its settings.
When you're on AUTO, in the dark the camera will automatically decide to go for the highest ISO settings it has. All it realises is: oooo, dark, need high ISO. That would be ISO400 for my Powershot, and photos taken at ISO400 with that little camera become noisy as hell! Incredibly, awfully noisy!
And I think, that is what happened to your first night photos, Sebastian.
Make yourself familiar with manually setting your camera.
Choose the smallest possible ISO.
Then a fairly small aperture (yes, even that!).
And then firmly fasten your camera to a tripod (vital for night photography, absolutely vital!), set the exposure time (it will be loooooooong, depending on how many light sources there are around you), set the camera on self-timer, and step back and have it expose all by itself, without your hands touching it in the process.
Try, and come back to show us what you got. OK? (Maybe a fence, top of a garden wall, table, railing, can help as makeshift tripod, but you need to firmly rest the camera on something stable).