Nanomechanical definition of the properties of composite specimens based on polylactic acid (PLA) was made in the present study. Research activities with accent on biodegradable polymer nanocomposites have fundamental significance originated from the worldwide plastic waste pollution. To receive hybrid nanocomposites with high level of homogeneity, the low cost and environmentally friendly melt extrusion method has been applied. The role of graphene nanoplatelets (GNPs) and multiwall carbon nanotubes (MWCNTs) as reinforcing nanoparticles dispersed in the polymer matrix was thoroughly investigated. Quasi-static nanoindentation analysis was enriched by performance of accelerated property mapping and nanodynamic mechanical testing in order to fully describe the nanoscale surface homogeneity and stress relaxation behavior of the nanocomposite specimens. That novelty of the research approach had a well-marked contribution over the detection of the new samples’ nanomechanical features as a function of the type of carbon nanofiller. Refined nanoscratch experiments uncovered the resistance of the materials against notches by means of measurement of the coefficient of friction and accurate estimation of the residual penetration depth.