Along with mood and energy deficits a dehydrated brain has to use a lot more energy to accomplish the same tasks, shows a study from King's College London.
Quote from Dehydration affects brain structure and function in healthy adolescents (2011):
It was recently observed that dehydration causes shrinkage of brain tissue and an associated increase in ventricular volume.
Dehydration following the thermal exercise protocol led to a significantly stronger increase in fronto-parietal blood-oxygen-level-dependent (BOLD) response during an executive function task (Tower of London) than the control condition, whereas cerebral perfusion during rest was not affected. The increase in BOLD response after dehydration was not paralleled by a change in cognitive performance, suggesting an inefficient use of brain metabolic activity following dehydration. This pattern indicates that participants exerted a higher level of neuronal activity in order to achieve the same performance level. Given the limited availability of brain metabolic resources, these findings suggest that prolonged states of reduced water intake may adversely impact executive functions such as planning and visuo-spatial processing.
Also according to an article on shape.com the energy usage of the brain increases, probably referring to "inefficient use of brain metabolic activity".
Why exactly does the brain shrink and increase energy usage after dehydration?