We analyzed the influence of 1/f noise in superconducting circuits on circuit operation using an analog circuit simulation. We devised a circuit simulation considering the 1/f noise using a conventional analog circuit simulator that can analyze the influence of thermal noises. In the circuit simulation, we used a passive filter that has a transfer function of -3 dB/oct to convert the Gaussian distributed white noise into the 1/f noise. We analyzed the gray zone characteristics of both the QFP and a singleflux-quantum current comparator considering both thermal and 1/f noises; the calculated gray zone width characteristics agree well with experimental results. Moreover, the influence of the 1/f noise is dominant in low operating speed regions for the QFP. These results indicate that the influence of the 1/f noise should be carefully considered to design superconducting circuits driven by a low-frequency clock.