It comes after this reference to inferiority, hence why I thought to change it:
"Despite my achievement of becoming a part of this much superior group, musically, the feeling of inferiority which I had experienced during my first lesson returned with a vengeance"
I'm assuming, then, that consistency is key here, and that I should use "inferiority" so that it's in line with the meaning mentioned earlier in this paragraph?
Inferiority would be a matter of comparison to others. The speaker is comparing his abilities to those of the other musicians. Inadequacy would be a matter of comparison to a standard. The speaker would be saying that his abilities fall short of what is required. In this context, though, you might hold that he views the ability to play as well as the others to be the minimum