Are you exporting the file as a JPEG? If so, choose a higher quality, or select a different file type such as a PNG or GIF.
It sounds like you're describing the artifacting that occurs as a result of JPEG compression. If not, feel free to include a sample what you're describing.
I'd also recommend looking into the Selective Quailty option in the Optimization panel. You can force text areas to retain higher quality/lower compression while still more heavily optiming the rest of an image.