We address optical amplification properties of quantum nanoparticles of the cadmium selenide/cadmium sulfide (CdSe/CdS) material system with different dimensionality of spatial confinement. CdSe/CdS core/shell quantum dots (QDs), core/shell quantum rods (QRs) and 5 monolayer thick core/crown nanoplatelets (NPLs) at ambient temperature are considered, exhibiting 0D, 1D and 2D spatial confinement dimensionality of the electronic system, respectively. Continuous films of all these nanoparticles are synthesised, and amplified spontaneous emission (ASE) spectra are measured under femtosecond pumping at wavelengths of 400 nm and 800 nm, respectively. The lowest threshold is found for NPLs and the highest for QDs, demonstrating the influence of the rod-like and plate-like CdS structures. To emphasize this effect, ASE is demonstrated also in CdSe/CdS QRs and NPLs under nanosecond pumping at 355 nm in the same material films. The amplification has been achieved without use of any feedback structure, emphazising the efficiency of the antenna effect. The pumping threshold fluences for NPLs and QRs are observed to be similar, but no ASE is observed in QDs up to the damage threshold of the nanoparticle layers. The length variation investigation with nanosecond pumping resulted in the gain coefficients of 29 cm -1 and 37 cm -1 for QRs and NPLs, respectively.