Nowadays, researchers have been on the lookout for eco-sustainable additives such as agro/industrial waste in concrete in order to offset the carbon footprint created by cement manufacturing. However, it has been said that the use of agro/industrial-waste-based cementitious materials in concrete improves its quality. However, this study compared the performance of hydrated lime and cement concrete replaced with 5% and 10% Costus englerianus bagasse ash and bagasse fibre for determining the mechanical properties (compressive and flexural strength). Moreover, compressive strength was evaluated on cubical specimens and flexural strength was evaluated on beam samples at 7, 14, and 28 days, respectively. Results showed that the compressive strength and flexural strength of the concretes increased with an increase in the curing age. Also, the compressive and flexural strengths of cement concrete were recorded by 65.38 MPa and 10.86 MPa at 0% bagasse ash or fibre, which performed better than concrete replaced with 5% and 10% bagasse ash and fibre at 28 days, respectively. Besides, the compressive strength of concrete was noted by 53.85 MPa and 48.92 MPa at 10% bagasse ash and 10% bagasse fibre, respectively, while the flexural strength was calculated by 6.86 MPa and 5.54 MPa at 10% bagasse ash and 10% bagasse fibre, respectively, which were higher than that of concrete produced with hydrated lime alone at 28 days. Thus, bagasse ash performed better than bagasse fibre ash as a partial replacement of cement or hydrated lime in concrete production. Therefore, Costus englerianus bagasse ash or bagasse fibre improved the performance of hydrated lime concrete at 5–10% replacement, but higher concrete strength would be obtained in cement replacement than hydrated lime.