Did you pay a deposit? If so, there also should have been a walk through checklist detailing the condition of the carpet at the beginning of the tenancy. If the carpet was not brand new when you moved in, and you didn't damage it beyond "normal wear and tear" then no, you should not be charged replacement costs.
If they sent you a deposit disposition telling you that you owe them money and you disagree, you have a couple of choices. You can wait to see if they sue you, or you can take them to small claims to get your deposit back. The judge can order them to pay you twice your deposit if they did not follow the rules, but charmingly, that section concludes that nothing prevents a landlord from suing an ex tenant for damage to the property caused by the tenant. Unfortunately, many landlords see this as an opportunity to increase their profit margin.
The rules are at RCW 59 18 260, 270 and 280. Good luck with this - Elizabeth Powell