Excellent adhesion of electrospun nanofiber (NF) to textile support is crucial for a broad range of their bioapplications, e.g., wound dressing development. We compared the effect of several low- and atmospheric pressure plasma modifications on the adhesion between two parts of composite—polycaprolactone (PCL) nanofibrous mat (functional part) and polypropylene (PP) spunbond fabric (support). The support fabrics were modified before electrospinning by low-pressure plasma oxygen treatment or amine plasma polymer thin film or treated by atmospheric pressure plasma slit jet (PSJ) in argon or argon/nitrogen. The adhesion was evaluated by tensile test and loop test adapted for thin NF mat measurement and the trends obtained by both tests largely agreed. Although all modifications improved the adhesion significantly (at least twice for PSJ treatments), low-pressure oxygen treatment showed to be the most effective as it strengthened adhesion by a factor of six. The adhesion improvement was ascribed to the synergic effect of high treatment homogeneity with the right ratio of surface functional groups and sufficient wettability. The low-pressure modified fabric also stayed long-term hydrophilic (ten months), even though surfaces usually return to a non-wettable state (hydrophobic recovery). In contrast to XPS, highly surface-sensitive water contact angle measurement proved suitable for monitoring subtle surface changes.