"Rendering" a background/wallpaper?

[Rhaonoa]

Hello again!
Now, I was wondering this one basic thing I just attempted doing out of boredom
so, let's say I found a cool image on some social media I'm in, and that I wanted to make a wallpaper/background for myself with it, and I've been working on it for few minutes;
once I'm done, I try to set it as my background, but guess what: it looks kinda pixelated and like if it was in low quality, while I look at it in paint.net, it looks completely fine. 

What can I do to get it to work properly and look "full HD/quality" for my background?
I already tried resizing and using templates, but it won't work.

Anyways, here's the picture, I didn't add too much detail or effect into it, or at least I wouldn't consider it anything at all; I'm not done with it, and I still need to get rid of the white dots around the character and other stuff alike, but I'd rather get this doubt out of my head before I work too much on it...yeah.

It looks fine in the Windows visor, paint.net, and everywhere else, but as my screensaver the quality goes lower or it gets pixelated, what can I do to fix it, or to make it higher quality as a background/wallpaper?

Thanks, and good luck!
PD; The character, and the drawing aren't of my creation, I haven't asked the creator for permission neither, but I was just using it to have something to use within my daily dose of randomly improvising with pictures, if asked, I'll take it down.

Edited September 25, 2014 by Rhaonoa

[Ego Eram Reputo]

Your screen is probably stretching the image to fill the available space.  You need to either work with a larger canvas (i.e. the same size as your screen) or set the wallpaper parameter so that it doesn't stretch the image (used to be called Center Image or something similar).

[MikeRobe]

Yep, as EER said - if it's pixelated, use a larger canvas. Resizing will only blur the image and make approximations, so you need to make sure from the start to use a larger canvas and scale it down if you need to.

[Rhaonoa]

Your screen is probably stretching the image to fill the available space.  You need to either work with a larger canvas (i.e. the same size as your screen) or set the wallpaper parameter so that it doesn't stretch the image (used to be called Center Image or something similar).

I resized the image, and not the canvas. 

What would be the different between both, and could I get a bit more specified answer on how to do so?

Thanks.

[MikeRobe]

Well, resizing the image does what it says on the tin. Resizing the canvas simply makes the canvas bigger without transforming the image in any way, even by size. All resizing the canvas will do is create white area around the image, while not changing the size of the image itself.