Can I claim a refund on the excess payment because I forgot to carry my Railcard?

Refunds 

No. The Railcard terms and conditions state that must carry it with you at all times if travelling with a Railcard-discounted ticket. If you do not have the Railcard with you at the time your ticket is inspected you will be liable to pay the difference between the price paid for your ticket and the full undiscounted fare. You may also be charged a penalty fare.  You will not be entitled to a refund of this charge even if you can provide a copy of the Railcard at a later date.