Blasters ended their campaign in 10th place with 17 points.
Igor Angulo scored a stoppage-time winner as FC Goa rallied to post a thrilling 2-1 win.
FC Goa tried their best through Igor Angulo and Ortiz to get the equaliser but Chennaiyin's defense was too tough to crack.
Aniket Jadhav's strike (53rs minute) was the difference between the two sides in what was the 500th game of the ISL.
This was Odisha's fifth defeat of the season and they are yet to record a win.
Santana's twin burst came in the 56th minute after SC East Bengal scored their first ever ISL goal through Jacques Maghoma in the 26th minute.
After three losses on the trot, laggards SCEB finally opened their account as they now have one point from four matches, while JFC moved to fifth place with six points from five games.
Nerijus Valskis struck a brilliant brace as Jamshedpur FC handed ATK Mohun Bagan their first defeat of the season in the Indian Super League.
It was heartening to see the centre-back pairing of Costa and Kone fighting valiantly and blunting the avalanche of attack.
They have brought in two overseas strikers - Guinean Idrissa Sylla and Ghanaian Kwesi Appiah - to sharpen their attack.