Future network architectures supporting 5G, 6G, Internet of Things (IoT), and fixed line networks face diverse service requirements in various scenarios, particularly by growing Ultra Low-Latency and Reliable Applications (ULLRA) such as: autonomous driving, remote surgery, augmented reality, virtual reality, IoT applications, etc. Network Function Virtualization (NFV) and Software Defined Networking (SDN) are two promising complementary solutions to meet diverse service requirements. In this study, we propose a novel application- and reliability-aware SFC embedding algorithm aiming to (a) decrease the latency and (b) increase the reliability of ULLRA. In this regard, we prioritize ULLRA as high priority SFC requests and reserve an amount of physical resources (bandwidth, memory, CPU) for embedding only high priority SFC requests to improve their latency and reliability. We formulate our proposed algorithm in the form of an Integer Linear Programming (ILP) optimization model to obtain optimal results. We also offer a heuristic algorithm to obtain near optimal results to reduce the execution time and make it usable for real-world networks. We consider constraints on maximum tolerable end-to-end delay, physical resource utilization (bandwidth, memory, CPU), and reliability. We examine our proposed SFC embedding algorithm in different test scenarios such as changing the number and the length of SFC requests, the proportion of reserved physical resources for high priority SFC requests, and the proportion of low-latency traffic flows to the total traffic flows. The results show that our proposed algorithms effectively improve the latency and reliability of ULLRA with minimal side effects on other applications compared to state of the art algorithms.