I put a red rug over the cream carpet and the dye bled. Landlord wants replacement of carpet. How do i define the value of carpet ?

In this instance, it's going to be the cost of replacing the carpet with similar quality.  It will probably be necessary to match all of that color carpeting that's connected, because dye lots are different and you can't just patch one dye lot in with another.

The landlord is entitled to have the premises be put in as good a condition as they were before you did this.  Carpet tends to be an expensive fix, and you're going to have accept that.