This type of error amplifier has never been my preference, even though some personalities advocate its use. I prefer the type 2 EA, that introduces a zero and helps boost the phase margin.
Anyway, to answer your question, look at the picture of the Bode plot and note that the resulting gain (in dB) is merely an addition of the top two. The gain above the crossover frequency is the "high-frequency" gain. As you can see, lowering it means bringing the Rf, Cf pole closer to the ESR zero. That will make the gain begin to drop faster after the crossover frequency and result in lower gain at higher frequencies.
Bringing the Rf, Cf pole close to the ESR zero effectively cancels that zero, but the actual goal of the pole is to make the high-frequency gain drop. If that pole did not exist, the gain would be flat from the ESR zero onwards. (Actually, another pole is sure to occur, at least from the opamp itself if not from other parasitics, but its frequency could be too high and uncontrollable.)
The low-frequency gain can only be improved by increasing the EA gain, that is increasing the Rf/Ri ratio, as can be seen from the picture. The flat portion of the EA characteristic is the EA gain and is only affected by Rf/Ri.
Note that I have not included any info on the phase relationships. That can be relatively easily added, just by following the definition of the phase shift at a certain frequency f, in the presence of a pole or zero at frequencies fp, fz respectively. If you do that, remember that the EA has a -180deg phase shift at low frequency, due to the inverting configuration.