What makes phenol an antiseptic, is it because of its acidity which may increase the proton concentration at cell membrane? I am unable to figure out the exact mechanism.
The main reason for phenol being antiseptic is it's effect on proteins which it denaturates. It also causes leakage of cellular membranes. See the paper in reference 1 for some details and a load of references. They say in the section on phenol:
Phenolic-type antimicrobial agents have long been used for their antiseptic, disinfectant, or preservative properties, depending on the compound. It has been known for many years (215) that, although they have often been referred to as “general protoplasmic poisons,” they have membrane-active properties which also contribute to their overall activity (120) (Table (Table22).
Phenol induces progressive leakage of intracellular constituents, including the release of K+, the first index of membrane damage (273), and of radioactivity from 14C-labeled E. coli (242, 265). Pulvertaft and Lumb (386) demonstrated that low concentrations of phenols (0.032%, 320 μg/ml) and other (nonphenolic) agents lysed rapidly growing cultures of E. coli, staphylococci, and streptococci and concluded that autolytic enzymes were not involved.