We present the first observations of HCO⁺(1–0) and HCN(1–0) emission in the northern filaments of Centaurus A with ALMA. HCO⁺(1–0) is detected in nine clumps of the Horseshoe complex, with similar velocities as the CO(1–0) emission. Conversely, HCN(1–0) is not detected, and we derive upper limits on the flux. At a resolution of ∼40 pc, the line ratio of the velocity-integrated intensities I_HCO+/I_CO varies between 0.03 and 0.08, while I_HCO+/I_HCN is higher than unity, with an average lower limit of 1.51. These ratios are significantly higher than what is observed in nearby star-forming galaxies. Moreover, the ratio I_HCO+/I_CO decreases with increasing CO-integrated intensity, contrary to what is observed in the star-forming galaxies. This indicates that the HCO⁺ emission is enhanced and may not arise from dense gas within the Horseshoe complex. This hypothesis is strengthened by the average line ratio I_HCN/I_CO < 0.03, which suggests that the gas density is rather low. Using non-local thermal equilibrium, large velocity gradient modelling with RADEX, we explored two possible phases of the gas, which we call ‘diffuse’ and ‘dense’ and are characterised by a significant difference in the HCO⁺ abundance relative to CO, respectively N_HCO+/N_CO = 10⁻³ and N_HCO+/N_CO = 3×10⁻⁵. The average CO(1–0) and HCO⁺(1–0) integrated intensities and the upper limit on HCN(1–0) are compatible with both diffuse (n_H = 10³ cm⁻³, T_kin = 15−165 K) and dense gas (n_H = 10⁴ cm⁻³, T_kin > 65 K). The spectral setup of the present observations also covers SiO(2–1). While undetected, the upper limit on SiO(2–1) is not compatible with the RADEX predictions for the dense gas. We conclude that the nine molecular clouds detected in HCO⁺(1–0) are likely dominated by diffuse molecular gas. While the exact origin of the HCO⁺(1–0) emission remains to be investigated, it is likely related to the energy injection within the molecular gas that prevents gravitational collapse and star formation.