Air India Airlines — missed connecting flight due to flight delay

I had booked my flight from goa to Patna via Mumbai from Goibibo for 15th Dec. But Air India flight no AI684 got delayed for almost one and half hour due to which I missed my next flight GoAir S8585. The respective airlines didn't arrange for my next flight and is not ready to take responsibility yet. I had to book flight all by myself for 16th Dec. I have lost so much of my time and money due to all this. This is serious issue and I want compensation for that from them.