The nuclear radio emission of low-luminosity active galactic nuclei (LLAGNs) is often associated with unresolved cores. In this paper we show that most LLAGNs present extended jet radio emission when observed with sufficient angular resolution and sensitivity. They are thus able to power, at least, parsec-scale radio jets. To increase the detection rate of jets in LLAGNs, we analyze subarcsecond resolution data of three low-ionization nuclear emission regions. This yields the detection of extended jet-like radio structures in NGC 1097 and NGC 2911 and the first resolved parsec-scale jet of NGC 4594 (Sombrero). The three sources belong to a sample of nearby LLAGNs for which high-spatial-resolution spectral energy distribution of their core emission is available. This allows us to study their accretion rate and jet power (Q jet) without drawing on (most) of the ad hoc assumptions usually considered in large statistical surveys. We find that those LLAGNs with large-scale radio jets (>100 pc) have Q jet > 1042 erg s–1, while the lowest Q jet correspond to those LLAGNs with parsec-scale (<=100 pc) jets. The Q jet is at least as large as the radiated bolometric luminosity for all LLAGN, in agreement with previous statistical studies. Our detection of parsec-scale jets in individual objects further shows that the kinematic jet contribution is equally important in large- or parsec-scale objects. We also find that the Eddington-scaled accretion rate is still highly sub-Eddingtonian (<10–4) when adding the Q jet to the total emitted luminosity (radiated plus kinetic). This indicates that LLAGNs are not only inefficient radiators but that they also accrete inefficiently or are very efficient advectors.