When you upload an image, WordPress creates different sized versions of the image, so that a 600 pixel-wide version is loaded in a 600 pixel-wide space, rather than the 3000 pixel-wide original (for example, of course) which would be burdensome on lower-speed connections (and especially mobile devices which are probably even displaying just a 300 pixel-wide space).
To do this, WordPress uses whichever image processing software your hosting provider has installed on your server. It prefers ImageMagick, which has generally great color reproduction, but will settle for GD Graphics Library. Here’s a direct comparison on the two from one of WordPress’s core developers: https://www.getsource.net/2012/12/one-quick-example-of-the-difference-imagick-makes/
Judging by your own compassion, I’d have to say that your server may only have GD Graphics Library installed, so I’d start by asking them to make sure that ImageMagick (and the Imagick extension) is installed and active on your server.
Next is the super-important bit though, like with Photoshop or any image editor, WordPress is at the mercy of whatever quality level defaults your hosting provider has set with ImageMagick and GD Graphics Library. If they have them set to 70% or lower, it doesn’t matter what library they’re using, the re-sized images are going to look rather lousy.
(The opposite also has drawbacks too. If the quality is set to 100%, just like with Photoshop, you might wind up with a smaller re-sized image that’s actually a larger file-size than original.)
If you get ImageMagick running on your server, or it’s already installed, and it doesn’t help (due to the defaults your hosting provider is enforcing), there are three things you can do to further enforce the quality of your images:
1. At settings -> Media set your size dimensions to 0, then install and activate this plugin: https://www.ads-software.com/plugins/disable-responsive-images/
This will effectively disable WordPress’s resizing system. Your images will no longer be resized by WordPress, but you’ll be effectively loading a huge original in a tiny space every time, slowing down your site dramatically, and putting it at the mercy of browser scaling (which may pixelate the image, but won’t affect colors).
2. The Photon CDN in Jetpack will optimize your images to much higher quality on their end and do the resizing. Your images will be optimized much better than ImageMagick or GD would, and bandwidth and server resources will be offloaded to WordPress.com’s servers, but you will be offloading your images to a third-party: https://www.ads-software.com/plugins/jetpack/
3. https://www.ads-software.com/plugins/ewww-image-optimizer/ offers higher quality optimization routines at the expense of much more complication.
