There is nothing to feel inferior about not knowing Hindi.
This goes to the pre-independence era where Rajaji (a Brahmin) was a staunch supporter of the introduction of Hindi as a medium of instruction in TN schools.
Periyar, a visionary, was of the opinion that English was the way to prosperity and to rescue the downtrodden from vicious circle of poverty and religious superstitions. Hence he opposed Hindi, and advocated implementation of English instead.
His supporters like M Karunanidhi, and others lent their voice, as their bread (they were full-time politicians unlike Periyar) depended on TN vote bank.
Now, the quality of English is a critical factor why MNCs open their BPOs mostly in southern states.
Of course for defence and other military purposes, Hindi could still be used, but remember that the South is still in a much more prosperous condition than the North, and once we even raised the issue of autonomy for TN, if not full secession from the Indian Union.
If at all people from North criticize your not knowing Hindi, it is due to their inherent bias.
Tamizh is a classical language, which can trace its roots to periods earlier than other contemporary Indian languages like Hindi. The quality of literature produced by Tamizhs is of such superior quality that it is renowned and is taught in universities worldwide. It is even part of the elite set of languages in which text is sent on a spacecraft in search of extra terrestrial life. This is not so in the case of any Northern language, including Hindi.
As regards people of AP, it is their geographical proximity to other Northern states, and due to which population migration happens both ways, they could know more than 2 languages. For Tamizhs, there is absolutely no inhibition in learning Hindi as a third language, but that is what it will continue to be, a third language. Tamizh language is too sacrosanct to be infected by other languages.