I'm able to see the compression in the pixelated patterns appearing in certain fills in the picture you posted, and I would say try not to compress it too much. Honestly I think slicing the image is the better way to go with uploading here for mobile optimization sake.
If you're using Photoshop, I'd recommend exporting everything to a 80% percent quality jpg. You compress it file-size wise without degrading the image quality a lot.