In high-precision optical measurements, squeezed vacuum states are a promising resource for reducing the shot noise. To utilize a squeezed vacuum, it is important to lock the phase of the local oscillator (LO) to the squeezed light. The coherent control sideband (CCSB) scheme has been established for the precise phase locking, while the previous CCSB scheme was designed for the squeezed vacuum generated with an optical parametric oscillator (OPO). Thus the previous CCSB scheme is not applicable to squeezing by a single-pass optical parametric amplifier (OPA), which is attractive for generating broadband squeezed vacuum states. In this study, we propose a variant of CCSB scheme, which is applicable to the squeezing by single-pass OPA. In this scheme, we inject pump light and frequency-shifted signal light into an OPA crystal in the same way as the previous CCSB scheme. The parametric process in the OPA crystal generates a squeezed vacuum, amplifies the signal light, generates an idler light, and causes the pump depletion reflecting the interference of the amplified signal light and the idler light. Through the lock-in detection of the pump depletion, we can phase-lock the injected signal light to the pump light. Then, after the heterodyne detection of the signal and the idler light, we get the error signal of LO and realize the precise phase locking of LO to the squeezed quadrature. We show the feasibility of the proposed scheme by deriving the signal-to-noise ratio (SNR) of the modulated pump signal. We experimentally demonstrate the proposed scheme on pulsed squeezing by a single-pass OPA.