Network virtualization in wireless sensor networks (WSNs) enables the utilization of shared sensing capabilities in many industrial Internet of Things (IIoT) applications. Efficient assignment of WSN resources can be achieved through virtual network embedding (VNE) while considering the quality of information (QoI) (as the accuracy of sensing), the quality of service (QoS) (as the reliability), and wireless interference handling constraints. The more the virtual networks can be mapped onto the substrate network, the more revenue the infrastructure provider will acquire. Therefore improving the acceptance rate of VNE is essential. However, this may lead to occupying more network resources and links and increase the cost, especially in dense networks. On the other hand, the shared and complex nature of VNE exposes WSNs to security risks. In this paper, we develop a novel offline distributed trust-aware virtual wireless sensor networks (DTA-VWSN) algorithm to maximize the virtual networks acceptance rate while minimizing the cost. Our proposed algorithm considers the QoI, QoS, and security, by adding required trust level constraints to virtual nodes and links and trust level constraints to the substrate counterparts. Since centralized algorithms suffer from scalability issues, this paper presents our new approach to the virtual network embedding problem in a distributed manner. In this paper, we use the techniques of multiagent systems as a well-known approach for distributed systems to scale these algorithms to network size. Our DTA-VWSN algorithm achieves a high-quality sub-optimal solution in a short duration, enabling us to investigate the tradeoff between solution quality and search time. Our algorithm is also evaluated in large-scale network scenarios to verify all enforced limitations by the WSN substrate. Simulation results show that DTA-VWSN improves the virtual network acceptance ratio, cost, and execution time in large-scale substrate networks. For instance, in a scenario with 150 substrate nodes and 6 VNRs, the accuracy of DTA-VWSN compared with the optimal value in terms of the VNR acceptance rate and the cost is 91.6% and 94.5%, respectively, while the execution time is 68.35% faster.