This paper investigates the secrecy performance of satellite networks in short packet communication systems under shadowed Rician fading (SRF). We derive a lower bound on the average achievable secrecy rate in the finite blocklength regime (FBL) and provide analytical insights into the impact of key secrecy-related performance indicators (KPIs). Monte Carlo simulations validate the theoretical framework, and demonstrate that increasing the blocklength and improving the legitimate receiver's signal-to-noise ratio (SNR) enhance secrecy, while a stronger eavesdropper degrades it. Additionally, we show that directional antenna patterns can effectively reduce information leakage and provide secure satellite communications in the short packet regime. These findings offer valuable guidance for designing secure and efficient satellite-based communication systems, particularly in IoT and space-based networks.