Hi Lynn, FHA loans allow up to a 6% Seller Credit. Typically, any seller credit is asked for during the offer process after an initial walk-thru of the property has taken place to adjust price. The best opportunity for adjusting price for the condition of the carpet may have passed, depending on the contract you signed and your contingency periods. Since the worst that can happen is being told "no", I would ask for the credit.
No matter what the answer comes back as, FHA loans also require that any health & safety issues be corrected as a condition of final loan approval. I would concentrate your focus on your property inspection report looking for health and safety issues, which are much more important. Perhaps, if health and Safety issues are found, you may be able to bundle in some money for the carpet as well if the first answer was no.
Best of luck, -Steve