Communication delays in mobile robot teleoperation adversely affect human-machine collaboration. Understanding delay effects on human operational performance and neurocognition is essential for resolving this issue. However, no previous research has explored this. To fill this gap, we conduct a human-in-the-loop experiment involving 10 participants, integrating electroencephalography (EEG) and robot behavior data under varying delays (0-500 ms in 100 ms increments) to systematically investigate these effects. Behavior analysis reveals significant performance degradation at 200-300 ms delays, affecting both task efficiency and accuracy. EEG analysis discovers features with significant delay dependence: frontal $\theta/\beta$-band and parietal $\alpha$-band power. We also identify a threshold window (100-200 ms) for early perception of delay in humans, during which these EEG features first exhibit significant differences. When delay exceeds 400 ms, all features plateau, indicating saturation of cognitive resource allocation at physiological limits. These findings provide the first evidence of perceptual and cognitive delay thresholds during teleoperation tasks in humans, offering critical neurocognitive insights for the design of delay compensation strategies.