Indigo Airlines - Check-in denied

Today morning I had an Indigo Flight from Kolkata to Visakhapatnam at morning ****. When I queued upto check in for the flight at ****, the queue was already too long. I waited for another ** min for any final call outs for Visakhapatnam Flight which seemingly didn't happen. The queue wasn't progressing too well, at **** I asked the support staff about my check in for the flight. She said it's already closed. She took me to a senior who said the same. He flatly said it can't be done even though it wasn't my fault that their management is so poor in organising at the passenger queue. I am a Defence Personnel and requested him if he could help me in this since I have to report on Duty by ****. However, he flatly rejected my request quoting it wasn't their fault I was late. This is the first time I have encountered such an incident where the flight staff have behaved so rudely to a request. Instead of trying to help me out, the staff personnel said you wait till **** and take the next flight at **** by paying the excess fare. Seems they purposedly want the stranded to pay fine for no reason of their own. The airline staff behave as if they are unto making a profit out of it.
I politely requested them if he could check again for my special circumstance which they didn't seem to care about. It is harassing passengers to pay more money. Moreover, early hour flight at **** would require me to wake up by ****. At the end when I was denied entry at the airport, it has become even more mentally harassing, even more because I couldn't join my unit. This kind of airline services is seriously uncalled for. I am not even asking for a refund, but the least expected is a better treatment when the fault is of the management itself.