The Internet-of-Things (IoT) landscape is expanding with new radio technologies. In addition to the Low-Rate Wireless Personal Area Network (LR-WPAN), the recent set of technologies conforming the so-called Low-Power Wide Area Networks (LP-WAN) offers long-range communications, allowing one to send small pieces of information at a reduced energy cost, which promotes the creation of new IoT applications and services. However, LP-WAN technologies pose new challenges since they have strong limitations in the available bandwidth. In general, a first step prior to a smart object being able to gain access to the network is the process of network access authentication. It involves authentication, authorization and key management operations. This process is of vital importance for operators to control network resources. However, proposals for managing network access authentication in LP-WAN are tailored to the specifics of each technology, which could introduce interoperability problems in the future. In this sense, little effort has been put so far into providing a wireless-independent solution for network access authentication in the area of LP-WAN. To fill this gap, we propose a service named Low-Overhead CoAP-EAP (LO-CoAP-EAP), which is based on previous work designed for LR-WPAN. LO-CoAP-EAP integrates the use of Authentication, Authorization and Accounting (AAA) infrastructures and the Extensible Authentication Protocol (EAP) protocol. For this integration, we use the Constrained Application Protocol (CoAP) to design a network authentication service independent of the type of LP-WAN technology. LO-CoAP-EAP represents a trade-off between flexibility, wireless technology independence, scalability and performance in LP-WAN.