Integrated Sensing and Communication (ISAC) is envisioned as a promising paradigm in the evolution of future wireless networks. In this paper, we investigate a joint allocation strategy for ISAC networks in Ultra-Reliable and Low-Latency Communication (URLLC). To fulfill the stringent latency requirement, transmissions are executed using finite block length (FBL) codes. To minimize the total error probability of sensing and communication, a joint resource allocation original problem is formulated. To address the formulated nonconvex problem, we first decompose it into two subproblems, and rigorously prove the convexity of each subproblem. Following the convexity characterizations, an efficient block coordinate descent (BCD) based algorithm is proposed which achieves a near-optimal solution. The simulation results substantiate the analytical finding, and provide insights into the trade-off between sensing and communication of ISAC networks in URLLC.