When a flexible plate is peeled off a thin and soft elastic film bonded to a rigid support, uniformly spaced fingering patterns develop along their line of contact. Although the wavelength of these patterns depends only on the thickness of the film, their amplitude varies with all material and geometric properties of the film and that of the adhering plate. Here we have analyzed this instability by the regular perturbation technique to obtain the excess deformations of the film over and above the base quantities. Furthermore, by calculating the excess energy of the system, we have shown that these excess deformations, associated with the instability, occur for films that are critically confined. We have presented two different experiments for controlling the degree of confinement: by prestretching the film and by adjusting the contact width between the film and the plate.