Artificial intelligence (AI)-based channel state information (CSI) feedback (CSF) is a promising technique for next-generation cellular networks, drawing interest from both academia and industry. This method uses an autoencoder to compress and reconstruct the channel matrix's eigenvector into a precoder, known as implicit CSI. The existing CSF mechanism also requires user equipment (UE) to estimate the signal-to-noise ratio using implicit CSI to adapt the channel quality indicator (CQI) for different modulation and coding schemes. However, AI-based implicit CSF presents significant challenges for CQI generation. Specifically, since the UE only has access to the original perfect CSI rather than the reconstructed CSI, coupled with the sample-level instability of AI, there is a non-negligible mismatch between the precoder known at the UE and that applied at the base station, thus significantly degrading the accuracy of CQI and affecting the transmission rate. Addressing this issue, we propose a proxy-based CQI generation algorithm for AI-based implicit CSF. A lightweight neural network is generated at the UE by knowledge distillation to imitate reconstructed CSI. Thus, the CSI mismatch on both sides is minimized at a low cost, facilitating accurate CQI generation. Simulation results confirm that the proposed algorithm improves CQI accuracy and leads to a 21.64% increase in data rate, all achieved with extremely low complexity.