Final answer:
The component of the servuction model that the inability to accept an American Express credit card affects is the Service processes, which includes payment systems and procedures. This can lead to customer dissatisfaction.
Step-by-step explanation:
The servuction model is a framework used to understand the elements involved in the service delivery process. In the scenario provided, where a customer attempted to pay with an American Express credit card but the service firm did not accept it, the component of the servuction model that negatively influenced the customer's experience is d) Service processes. This component includes the mechanisms or procedures through which services are consumed, such as payment systems. The inability to process a payment through a commonly accepted credit card can lead to customer dissatisfaction and is related directly to the service processes put in place by the company.