Images edited in Illustrator lose quality after uploading to my gaming website

skilful,

It is difficult to be sure without seeing both an Ai screenshot and the resulting PNG. Can you post both together, using the Insert Photos button at the top of the Reply box (looks like moon over mountains) so they can be seen directly in your post?

With regard to colours, are you exporting/saving (for web) as PNG 24 to get all the usual colours, or as PNG 8 corresponding to GIF? This could make a decisive difference; see also below about getting the colours right.

Sorry if the following writ sounds unforgivably outdated and boring, covering a number of aspects. Some of it may be relevant in connexion with sharpness, and also a bit abou getting the colours right.

If you wish to have PNGs (PNG24 (also (little) known as PNG32, it holds 24 bit colour and 8 bit Alpha channel (transparency)), of course) look crisp and clean, at least when it is (also) to be used at moderate screen resolutions, it is important to have the images in the exact desired final pixel x pixel size, or at sizes that are powers of 2 times as large, in other words 2x, 4x, 8x, and so on: the larger values can improve the appearance on high resolution screens and still ensure best possible appearance at low resolution screens, owing to controlled downsampling that gives exactly the same colour in each pixel at 1x as when created at 1x; or work at 72PPI or powers of 2 times as large (144PPI, 266PPI, 576PPI, and so on).

Forget about print related image resolution such as 300PPI which may actually lead to wrong sizes and hence blurriness, and to colour issues by uncontrolled downsampling.

It is easiest and safest to work at the desired size when creating the artwork.

It is important to remember that a raster image represents the whole appearance, including strokes, so to make sure you get it right you can click Use Preview Bounds in the General Preferences (and untick it afterwards).

A very common unsuitable way is to Export to PNG (remember to use PNG24 and use Transparency for artwork to be in front of different backgrounds) with a medium or high resolution, such as 300PPI.

And a common misunderstanding: (almost) 11 out of 10 times, a statement like "I created the document at 300 PPI" means that the value is chosen in Effect>Document Raster Effects Settings; however that only means that the (current) resolution of any raster effects applied to the vector artwork, such as (any kind of) Blur, is set to that value (and only unless/until the value is changed to something else); when zooming in, this resolution can be seen in contrast to and on the background of the vector artwork. So this setting has nothing whatsoever to do with the actual resolution of a raster image created from the (vector) artwork (but it ought to (at least) match it).

For clean and crisp artwork avoid JPEG; to get the colours right, you may wish/need to finalize by opening the PNG in PS (Photoshop) and attach the (missing) colour profile (such as sRGB) there.

It is also important to have the artwork and also the Artboard(s) placed fully within integer/whole pixel X and Y values in the Workspace, which means that the X and Y values at the corners must be integer; this can be ensured by using one of the corner Reference Points in the Transform palette, and then checking that all the values X, Y, W, and H, are integer (the centre Reference Point can only be used if both W and H are even numbers).

If you have issues with the Artboard(s), make sure the rulers are Global Rulers (RightClick), if not change from Artboard to Global Rulers; and to align your artboards, click the Rearrange All Artboards button in the Artboards panel. First posted by Ton here,
https://community.adobe.com/t5/illustrator-discussions/why-is-illustrator-not-exporting-artboard-size/m-p/13350220#M343886

Otherwise the resulting image will become a bit wider/taller and the extension(s) will be empty and therefore be (partially) transparent/white.

Therefore, a safe way is to create the artwork at the final pixel x pixel size and use a corresponding Artboard, then use the Legacity Save for Web (where you can look in the Image Size window for size confirmation and possibly multiply by 2, 4, 8, whatever), or use Export at 72PPI (or 144/288/576/whatever PPI), or use Export for Screens (in either way). In either case, use the relevant optimization (available with both ways); it is also convenient to have 72PPI (or 144/288/576/whatever PPI) in the Effect>Document Raster Effect Settings.

If you have pure vector artwork, you can relax a bit and have the artwork/Artboard at any size (the Artboard must have the same proportions as the final image), then use the Legacity Save for Web and set either Width or Height in the Image Size and Apply (make sure the other value is also correct).

The Legacy Save for Web may be an old carthorse, but it knows its way home, even if the driver is drunk and sleeping it off in the hay in the back.

Or you can switch to SVG, if applicable.

https://helpx.adobe.com/search-results.html?q=svg&scope=%5B%22helpx%22%5D&subscope=%5B%5D&limit=10&start_index=0&sort_orderby=relevancy&sort_order=desc&post_facet_filters=%7B%22applicable_products%22%3A%5B%5D%7D

Those are mostly photos in your screenshot. You are just trying to attract visitors to your website?