Background: Depressive symptoms are frequent sequelae of COVID-19 and may remain unrecognized in older outpatients, particularly those with post-COVID syndrome. The objective of the current study was to assess the under-detection of depressive symptoms in older ambulatory patients and to examine its relationship with post-COVID syndrome status. Methods: We conducted an observational outpatient cohort study of adults aged 60–89 years with prior SARS-CoV-2 infection (N = 85), recruited at two city polyclinics. Depressive symptoms were assessed through three detection channels: spontaneous complaint during the visit, a standardized direct question about current depressive symptoms, and the 15-item Geriatric Depression Scale (GDS-15). Agreement between complaint and direct question was evaluated using Cohen’s κ and McNemar’s test. Screening performance of complaint and direct question was assessed against GDS-15 thresholds (≥5; sensitivity analysis ≥ 6). Associations between post-COVID syndrome status and binary depressive-symptom indicators were expressed as risk ratios (RRs). Results: Spontaneous complaints missed a substantial proportion of cases: among complaint-negative patients, 18.3% (15/82) reported depressive symptoms on the direct question (κ = 0.149; McNemar p = 0.00052). Against GDS-15 ≥ 5, complaint sensitivity was 10.3% with specificity 100.0% (F1 = 0.19), whereas the direct question showed higher sensitivity (34.5%) with specificity 87.5% (F1 = 0.43). Using the alternative threshold GDS-15 ≥ 6, complaint sensitivity was 15.0% with specificity 100.0% (F1 = 0.26), and direct question sensitivity was 45.0% with specificity 87.7% (F1 = 0.49). A positive response to the direct question was more frequent in patients with post-COVID syndrome than in controls (RR = 2.70 (1.04–7.00)); stratified estimates suggested higher RRs in patients ≤ 75 years (RR = 4.55 (1.08–19.10)) and in women (RR = 2.67 (1.04–6.83)), with limited precision due to sparse events. Conclusions: In older post-COVID outpatients, reliance on spontaneous complaints leads to marked under-detection of GDS-15 screen-positive depressive symptoms. A standardized direct question improves initial case-finding but does not replace a validated screening scale; a stepped approach (brief direct question followed by a scale when indicated) may be warranted.