The disc diffusion method relies on diffusion of the active substance into the agar, establishing a concentration gradient of decreasing concentration with increasing concentration from the disc. I would suppose that the nanofibre film is not going to diffuse from the disc, so you are relying on the antibacterial component to diffuse out if the nanofibre film. If this does not happen very well, then no zone of inhibition will be seen. Clearly there is a need to measure the concentration of the antibacterial component in the agar at various distances from the disc to find out if the component has diffused or not.

Thank you Adam B Shapiro sir for your valuable suggestion. Can you suggest me how can we measure the concentration of the antibacterial component in the agar?

Can i keep my nanofibre film in water for few hours to make the active substance diffuse from the film?

I don't know anything about the stability in water of your nanofibre film.

To measure the agar MIC, you could mix the nanofibre film in at various concentrations with some melted top agar and pour it onto  agar plates. Each plate would then have a different concentration of nanofibre film in the agar.

In my experience for the antibacterial effect the surface of the bacterial cell must be covered with carbon-based nanoparticles from all sides. Films not produce this effect if particles do not diffuse.

Earlier we saw same effect for graphene oxide: active GO particles but the GO paper is not (Toxicity of Graphene Shells, Graphene Oxide, and Graphene Oxide Paper Evaluated with Escherichia coli Biotests).

My nanofibre film is the derivative of chitosan which itself has the antimicrobial effect and its a carbon based compound .

Where on earth it has been encrypted that the expected results of research (which you have prethought) must come true, or else your investigation is wrong.