Background/Objectives: Postbiotics derived from lactic acid bacteria are emerging as promising antimicrobial agents due to their antibacterial, antibiofilm, and immunomodulatory properties. Among their metabolites, lactic acid (LA) is thought to play a major role in antimicrobial activity. This study investigated the proteomic response of Pseudomonas aeruginosa and Staphylococcus aureus to Lacticaseibacillus rhamnosus cell-free supernatant (CFS) and compared it with that elicited by LA alone. Methods: Overnight bacterial cultures were exposed to sub-MIC LA or CFS (1:10 for P. aeruginosa and 1:8 for S. aureus; ~12.5–15.6 mM LA) for 6 h at 37 °C. Intracellular proteins were harvested and subsequently quantified and purified to be analysed by HPLC–MS/MS, for quantitative label-free proteomics. Results: Proteomic analysis revealed clear separation of treated samples from controls, with largely overlapping responses to CFS and LA. Hallmark acid-stress adaptations were observed, including urease-mediated pH buffering, confirming that part of the response was driven by mild organic acid. In P. aeruginosa, treatments suppressed virulence pathways (phenazines, T3SS), while shifting metabolism toward lactate utilisation and reinforcing the outer membrane (lipid A, polyamine). In S. aureus, decreased abundance of the SaeRS-regulated immune-evasion factor Sbi, together with changes in envelope, ROS and translation-related proteins, suggested a bacteriostatic-like state. S. aureus differences between CFS and LA were more pronounced; CFS uniquely increased cell-wall defences, oxidative stress (SodA, SodM) and chaperone expression (GroS, GrpE), suggesting stress beyond acidification alone. Conclusions: These findings shed light on the molecular mechanisms underlying bacterial adaptation to CFS and highlight their potential as a novel antimicrobial approach.