Is this expression correct "the reaction was not accomplished " when we check the final product finding two or more spots on TLC paper ?
Because "finding two spots" was difficult to understand, my answer to this includes an idealized graphical representation of a TLC. It consists of two lanes A, and B for two starting materials. There is a reference lane (D) of the already known, confirmed and purified product -- for example obtained by a previous batch of synthesis, or (as met once in lab classes) the TA offers to spot it, using his/her known reference.
If lane C was used to co-spot both the starting material(s) as well the reaction product, yet you do not detect (by UV-Vis, or derivatization) a spot corresponding in $R_f$-value to your reference (in lane D), than your analyte analyzed does not contain significant amounts of your intended product.
Depending on how / if at all a work-up prior to spotting the sample of the unknown was executed, this observation indeed may refer to "the chosen conditions did not yield significant amounts of the intended product".
Yet if you forgot to quench/neutralize (and subsequently extracted) your analyte sample prior to spotting, your product may be still at the ground line -- esp. for salty samples on a silica TLC -- and hence not elute at $R_f = 0.75$. Second potential pitfall I imagine: you quench your reaction with water, and extract at different pH values (separation of strongly acidic / acidic / basic compounds) -- your intended product simply is in the subsequent extract that accidentally was not spot on lane C.
The TLC was idealized that the compounds would nicely separate from each other, without any smearing/fronting/tailing either individually, nor in presence of each other (+ other components of the reaction mixture not detected by the TLC [e.g. solvent(s)]). Simultaneously, it is assumed there is no decompostion of any of the products while eluting the TLC, that could be checked by 2D-TLC.