The advent of network softwarization is enabling multiple innovative solutions through software-defined networking (SDN) and network function virtualization (NFV). Specifically, network softwarization paves the way for autonomic and intelligent networking, which has gained popularity in the research community. Along with the arrival of 5G and beyond, which interconnects billions of devices, the complexity of network management is significantly increasing both investments and operational costs. Autonomic networking is the creation of self-organizing, self-managing, and self-protecting networks, to afford the network management complexes and heterogeneous networks. To achieve full network automation, various aspects of networking need to be addressed. So, this article proposes a novel architecture for the multi-agent-based network automation of the network management system (MANA-NMS). The architecture rely on network function atomization, which defines atomic decision-making units. Such units could represent virtual network functions. These atomic units are autonomous and adaptive. First, the article presents a theoretical discussion of the challenges arisen by automating the decision-making process. Next, the proposed multi-agent system is presented along with its mathematical modeling. Finally, MANA-NMS architecture is mathematically evaluated from functionality, reliability, latency, and resource consumption performance perspectives.