A three-level system based an a three-level atom interacting with a detuned cavity is considered. Because of the fact that the three-level atom defines a total normalized state composed of superposition of three different single-level states, it is assumed that such a system implements a qutrit. In order to achieve a quantum NOT gate for a single qutrit, the respective Schrödinger equation is solved numerically within a two-photon rotating wave approximation. For small values of one-photon detuning, there appear decoherence effects. Meanwhile, for large values of onephoton detuning, an ideal quantum NOT gate for a single qutrit is achieved. An expression for the execution time of the quantum NOT gate for a single qutrit as a function of the one-photon detuning is found.