I had a different experience with Indigo. When I tried to use my Chase visa the portal rejected it. I checked with Indigo, then determined it was the bank. I called the bank twice before it was resolved. My amex was rejected too but I did not try to resolve this.
The same thing happened to my brother when he tried to book on Paramount. After repeated tries, it only accepted the Indian CC.
There should be a procedure to register the foreign credit cards.
However other merchants in India routinely accept foreign credit cards and the charges go through without any problems (hotels, department stores, restaurants etc.). It seems the problem is unique only with airline websites.