The nuclear radio emission of LLAGN is often associated to unresolved cores. In this paper we show that most LLAGN 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 LLAGN, we analyze sub-arcsec resolution data of three LINERs. This yields the detection of extended jet-like radio structures in NGC\,1097 and NGC\,2911 and the first resolved pc-scale jet of NGC\,4594 (Sombrero). The three sources belong to a sample of nearby LLAGN for which high-spatial-resolution SED of their core emission is available. This allows us to study their accretion rate and jet power (Q$_\mathrm{jet}$) without drawing on (most) of the ad-hoc assumptions usually considered in large statistical surveys. We find that those LLAGN with large-scale radio jets ($>$ 100 pc) have Q$_\mathrm{jet} > 10^{42}$ erg s$^{-1}$, while the lowest Q$_\mathrm{jet}$ correspond to those LLAGN with pc-scale ($\leq$ 100 pc) jets. The Q$_\mathrm{jet}$ is at least as large as the radiated bolometric luminosity for all LLAGN, in agreement with previous statistical studies. Our detection of pc-scale jets in individual objects further shows that the kinematic jet contribution is equally important in large- or pc-scale objects. We also find that the Eddington-scaled accretion rate is still highly sub-Eddington ($<10^{-4}$) when adding the Q$_\mathrm{jet}$ to the total emitted luminosity (radiated plus kinetic). This indicates that LLAGN are not only inefficient radiators but that they also accrete inefficiently or are very efficient advectors.