Detection of subtle deficits in everyday functioning due to cognitive impairment is important for early detection of neurodegenerative diseases, particularly Alzheimer's disease. However, current standards for assessment of everyday functioning are based on qualitative, subjective ratings. Speech has been shown to provide good objective markers for cognitive impairments, but the association with cognition-relevant everyday functioning remains uninvestigated. In this study, we demonstrate the feasibility of using a smartwatch-based application to collect acoustic features as objective markers for detecting deficits in everyday functioning. We collected voice data during the performance of cognitive tasks and daily conversation, as possible application scenarios, from 54 older adults, along with a measure of everyday functioning. Machine learning models using acoustic features could detect individuals with deficits in everyday functioning with up to 77.8% accuracy, which was higher than the 68.5% accuracy with standard neuropsychological tests. We also identified common acoustic features for robustly discriminating deficits in everyday functioning across both types of voice data (cognitive tasks and daily conversation). Our results suggest that common acoustic features extracted from different types of voice data can be used as markers for deficits in everyday functioning.