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The limited bandwidth of underwater acoustic channels poses a challenge to the efficiency of multimedia information transmission. To improve efficiency, the system aims to transmit less data while maintaining image utility at the receiving end. Although assessing utility within compressed information is essential, the current methods exhibit limitations in addressing utility-driven quality assessment. Therefore, this letter built a Utility-oriented compacted Image Quality Dataset (UCIQD) that contains utility qualities of reference images and their corresponding compcated information at different levels. The utility score is derived from the average confidence of various object detection models. Then, based on UCIQD, we introduce a Distillation-based Compacted Information Quality assessment metric (DCIQ) for utility-oriented quality evaluation in the context of underwater machine vision. In DCIQ, utility features of compacted information are acquired through transfer learning and mapped using a Transformer. Besides, we propose a utility-oriented cross-model feature fusion mechanism to address different detection algorithm preferences. After that, a utility-oriented feature quality measure assesses compacted feature utility. Finally, we utilize distillation to compress the model by reducing its parameters by 55%. Experiment results effectively demonstrate that our proposed DCIQ can predict utility-oriented quality within compressed underwater information.