We study thermodynamic limits when controllers operate with only partial observability of internal correlations in multipartite systems. Understanding the costs imposed by lack of information is crucial in settings where agents must act under incomplete knowledge, and clarifying the thermodynamics of the intertwined sense-act feedback remains a central challenge. We consider a single-step stochastic evolution of a classical multipartite system coupled to a single heat bath under protocols that do not generate new inter-subsystem correlations, and we allow arbitrary reciprocal interaction topology. From Clausius-type local inequalities for each component, we sum and recast the result into an information-theoretic form that isolates the role of inaccessible correlation changes. We thereby obtain a generalized second law: the total entropy production is bounded below exactly by the decrease of internal correlations that is inaccessible to any controller whose state is not included in the relevant information set; only the accessible part can, in principle, be diverted from dissipation. The result refines standard bounds without invoking measurement updates and characterizes information as an indispensable resource: correlations become work-relevant precisely to the extent that they are known, while the unknown portion is unavoidably dissipated.