For achieving perfect absorption (PA), the absorbing film usually has either high loss or a thickness much greater than its wavelength. We propose a simple bilayer structure composed of a perfect electric conductor substrate and an indium tin oxide (ITO) film to solve the situation. Results show that PA can be realized with a film thickness of several nanometers based on the epsilon-near-zero (ENZ) response and relatively low loss of ITO film. Notably, PA at different thicknesses of the film can be achieved by simply selecting the appropriate incident angle, and it is further demonstrated that the incident angle should be reduced linearly with an increase of the thickness of the film to maintain PA. Furthermore, the ENZ wavelength can be flexibly controlled by changing the carrier density via electrostatic field, resulting in the tunability of PA. These adjustable simple and tiny perfect absorbers may find practical applications in photodetectors and sensors.