Video Pixelated After Export

I'm fairly new to Adobe Premiere, and I'm really stumped as to what the problem could be here. And maybe it's just as good as it gets...

So after exporting the mp4 file in Premiere, the video looks somewhat pixelated. There is a lot of smoke in the video, and subtle gradients, and the video seems to have sort of distinct sections of color, that are a bit pixelated. In premiere itself, it looks absolutely perfect, but not in the exported version. I'm wondering if that's just the way it is, and I need to accept that it doesn't look as good as in Premiere?...

Here is a screenshot of what the video looks like in Premiere:

And here is one of the first frame in Quicktime player, of the exported version:

It's kind of hard to tell in these photos, but you can see defined sections in the bottom one, where it kind of looks like Quicktime is just rounding certain pixels off, and it's not just a completely smooth gradient. And it's kind of pixelated... not absolutely horrible, but nowhere near as good as in Premiere.

Here is what my export setting look like:

And then further down:

I've also tried exporting through Media Encoder, and that seemed to make no difference. (I have Encoder open during these screenshots, which is why there's no 'Export' button I believe, to do it within Premiere)

Any thoughts on a possible solution would be amazing! The final video will basically just go on to Youtube... if that matters...

Thanks very much in advance!