Approximate the change in perceived gain from applying transfer function to audio signal
You want to calculate loudness difference between input and output. 

Loudness depends on the power spectral density of a signal; knowing only the transfer function of your filter is not enough for calculating PSD.

For example, suppose your filter is a lowpass filter, with attenuation 20 dB in the stop band. If your input signal is completely contained below the cutoff frequency, then no perceived gain (input and output are similar), whereas if your input signal is all above the cutoff frequency, then you will perceive a -20dB gain.

Related question on calculating loudness.