It may actually be due to the fact that you're sitting a lot closer to the monitor than you would be to a large tv, proportionally speaking. Also, there may be a variance in pixel density do to the size difference of both your tv and monitor that may also contribute to why you are seeing a grainier image. I have a 23" 1080p ASUS monitor and a 60" Samsung ES8000 3DTV and I too notice that the monitor is grainier because I am sitting up close and I notice the pixels a lot more.
Unless your monitor is significantly bigger than mine and/or of a lower resolution, I don't think there is anything much you can do other than sitting further back while viewing media on your monitor.