GoPro video lose color quality while exporting in Premiere CC
This might indeed be a dupe of Upon export in Premiere Pro, colors lose saturation when previewing in QuickTime.

Are you using QuickTime .mov as your video container or MP4? If it's the former you will find your solution in the answer above.

If not, this might just have to do with your settings when encoding to h264. Try to export in a lossless codec and see if you get the same result. Then try an application like Handbrake with High Profile and see if you still get the same issue. H264 is a lossy codec and with a low-bitrate you can get washed out colors.