We numerically study the interaction of a terahertz pulse with monolayer graphene. We use a numerical solution of the two-dimensional Dirac equation in Fourier space with time-evolution based on split-operator method to describe the dynamics of electron-hole pair creation in graphene. We notice that the electron momentum density is affected by the carrier-envelope phase (CEP) of the few-cycle terahertz laser pulse that induces the electron dynamics. Two main features are observed: (1) interference pattern for any values of the CEP and (2) asymmetry, for non-zero values of the CEP. We explain the origin of the quantum interferences and the asymmetry within the adiabatic-impulse model by finding conditions to reach minimal adiabatic gap between the valence band and the conduction band in graphene. The quantum interferences emanate from successive non-adiabatic transitions at this minimal gap. We discuss how these conditions and the interference pattern are modified by the CEP. This opens the door to control fundamental time-dependent electron dynamics in the tunneling regime in Dirac materials. Also, this suggests a way to measure the CEP of a terahertz laser pulse when it interacts with condensed matter systems.