We analyzed frequency-domain characteristics of a femtosecond laser whose carrier-envelope phase (CEP) was stabilized by the direct locking method (DLM). To evaluate the CEP-stabilized laser with zero carrier-envelope-offset frequency (f(ceo)), as imposed by DLM, a self-referencing f-to-2f interferometer with a shifted frequency comb by an acousto-optic modulator was employed in an out-of-loop. The measurement of the square root of triangle variance confirmed that DLM is a phase-locking method. The tight locking was verified from a narrow bandwidth of f(ceo), measured using the out-of-loop interferometer, and from a small frequency jitter measured with a frequency counter referenced to a Rb-clock. The femtosecond laser with CEP stabilized by DLM is, thus, well suited for applications in the frequency domain as well as in the time domain.