Oral function (OF) decline in older people is associated with nutritional deficiencies, which increases frailty risk and the need for nursing care. We investigated whether the delivery of an oral function improvement program on a tablet device was as effective as delivery through a paper-based program. We also investigated the association between tongue pressure (TP) improvement and nutritional status at the baseline. The participants involved in the study were 26 community-dwelling older people with low TP, <30 kPa, aged ≥65 years, who were enrolled in a randomized controlled trial for a month in Itoshima City, Fukuoka, Japan. Oral and physical functions and body composition were measured at the baseline and at follow-up. Two-way analysis of variance revealed that body mass index (p = 0.004) increased, and maximum masticatory performance (p = 0.010), maximum TP (p = 0.035), and oral diadochokinesis /pa/ and /ka/ (p = 0.009 and 0.017, respectively) improved in a month. Participants with higher TP improvement showed an increased intake of animal proteins at the baseline: fish (p = 0.022), meat (p = 0.029), and egg (p = 0.009). OF exercises for improving TP were associated with higher animal protein intake at the baseline. This study has been registered with the UMIN Clinical Trials Registry (UMIN 000050292).