We propose uplink power control (PC) methods for massive multiple-input multiple-output systems with 1-bit analog-to-digital converters, which are specifically tailored to address the non-monotonic data detection performance with respect to the transmit power of the user equipment (UE). Considering a single UE, we design a multi-amplitude pilot sequence to capture the aforementioned non-monotonicity, which is utilized at the base station to derive UE transmit power adjustments via single-shot or differential power control (DPC) techniques. Both methods enable closed-loop uplink PC using different feedback approaches. The single-shot method employs one-time multi-bit feedback, while the DPC method relies on continuous adjustments with 1-bit feedback. Numerical results demonstrate the superiority of the proposed schemes over conventional closed-loop uplink PC techniques.