The trapping mechanism at the AlGaN/GaN interface in the p-GaN high electron mobility transistors (HEMTs) and its impact on the turn-on characteristics of direct-coupled FET logic (DCFL) inverters were investigated across various supply voltages (VDD) and test frequencies (fm). The frequency-conductance method identified two trap states at the AlGaN/GaN interface (trap activation energy Ec-ET ranges from 0.345 eV to 0.363 eV and 0.438 eV to 0.47 eV). As VDD increased from 1.5 V to 5 V, the interface traps captured more electrons, increasing the channel resistance (Rchannel) and drift-region resistance (Rdrift) of the p-GaN HEMTs and raising the low-level voltage (VOL) from 0.56 V to 1.01 V. At fm = 1 kHz, sufficient trapping and de-trapping led to a delay of 220 µs and a VOL instability of 320 mV. Additionally, as fm increased from 1 kHz to 200 kHz, a positive shift in the threshold voltage of p-GaN HEMTs occurred due to the dominance of trapping. This shift caused VOL to rise from 1.02 V to 1.40 V and extended the fall time (tfall) from 153 ns to 1 µs. This investigation enhances the understanding of DCFL GaN inverters’ behaviors from the perspective of device physics on power switching applications.