It sounds like you're using custom settings or a preset that's not a good match for what you're expecting of you rendered movie file.
Try going one of theses two options:
Chose File > Export Using Render Queue. In the Render Queue, set the Render Setting to Best and the Output Module to Lossless (these are the defaults and will probably already be selected). This file will be very close, if not the same, image quality as the original Comp; however, it will be very large (that is, it will take up a lot of disk space) and it will only play smoothly from high bandwidth storage. If you need an alpha channel (for say, an animated logo), change the Output Module to Lossless with Alpha.
Or,
Chose File > Export Using Adobe Media Encoder Queue. In the Queue tab for Adobe Media Encoder (AME), set the Format to H264, set the Preset to Match Source - High Bit Rate. This creates a high bit rate MP4 file that should have very good image quality and the file will play back from just about anything (but not exactly everything) that supports the MP4 file format.
-Warren