We theoretically investigate the effects of the carrier-envelope phase of few-cycle laser pulses in the multiphoton ionization regime. For atoms with low ionization potential, total ionization yield barely exhibits phase dependence, as expected. However, population of some bound states clearly shows phase dependence. This implies that the measurement of the carrier-envelope phase would be possible through the photoemission between bound states without energy-and-angle-resolved photoelectron detection. The considered scheme could be particularly useful to measure the carrier-envelope phase for a light source without an amplifier, such as a laser oscillator, which cannot provide sufficient pulse energy to induce tunneling ionization.