Assuming you paid money for the ticket then, yes, you are due a refund. Gagravarr links to the EU rules (EU261) but there's also Air India's Conditions of Carriage [PDF], which states:
Carrier does not guarantee to provide any particular seat in the aircraft and the passenger agrees to accept any seat that may be
allotted on the flight in the class of service for which the ticket has been issued.
Which would then mean that the following section should apply:
11.3 INVOLUNTARY REFUNDS
If Carrier cancels a flight, fails to operate a flight reasonable according to schedule, fails to stop at a point to which the
passenger is destined or ticketed to stop over, is unable to provide previously confirmed space or causes the passenger to
miss a connecting flight on which the passenger holds a reservation, the amount of the refunds shall be:
11.3.1 If no portion of the ticket has been used, an amount equal to the fare paid;
11.3.2 If a portion of the ticket has been used, the refund will be the higher of;
11.3.3 The one way fare (less applicable discounts and charges) from point of interruption to destination or point of next
11.3.4 The difference between the fare paid and the fare for the transportation used.
Also, they in section 3 it implies that they should have offered you a seat on the next flight with business class space, rather than bumping you down to economy.
Finally their FAQ states that you both get a refund and how to get it:
Q.If I have been downgraded on my flight, do I qualify for a refund?
In case of involuntary downgrading, due to a change in aircraft, after completion of travel, you need to send the ticket jacket with the boarding cards to the Refunds section and as per the applicable fare rule a refund will be processed. In case of a downgrade and if you are transferred to any other airline the case is treated as a ‘transportation credit’ where a message has to be sent to the respective airline, our Central accounts and the IATA billing section, and only then is the refund processed. The ticket copy and the boarding card also need to be sent for this refund.
Although that does say 'change of aircraft' I think taking all of these together makes it clear that if you paid for the flight you're due a refund. If you purchased the flight, or an upgrade, using frequent flier miles then I'd expect the most you can hope for is to get (some of) them refunded. However, if you were upgraded by the airline for free then I doubt you have any rights to a refund.
You say it wasn't your seat that was broken, I'm guessing what happened here is that there's an issue with a business class seat and whoever is in charge decided to either bump the person with the cheapest ticket and/or the person they thought would cause least fuss. Or possibly the person who has least evidence of flying regularly.
None of that means that they shouldn't refund you something, which means the question is how to get the refund.
As it says above you need to submit the required documents, if you don't have them anymore I'd try calling someone in the customer service center, the numbers are on the contact page. Explain what happened, have dates and flight numbers available. It may be useful to call first even if you have the documents and ask if submitting electronic versions of the documents is acceptable. I'm not sure it's worth mentioning the attitude of the duty manager as it looks like their process is quite clear and the amount of the refund is probably fixed.
That's the process you should follow, but be aware that it may take a fairly long time to get any money back. One other thing you could consider doing is sending them a message on Twitter. Something like
@airindiain Bumped from business to econ, AIxyz on xTh Sept, manager very rude, no refund offered, terrible way to treat a senior citizen
That's just under the character limit. That way you make the complaint public, and I doubt any company will want to let something like that go unanswered for very long.