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Striker Dimitrios Diamantakos, who was the Blasters' leading goalscorer last season, had announced his departure.
The loss also crushed Mohun Bagan's dream of becoming the first team to defend the ISL Cup and complete a rare double of winning the League Winners' Shield and the title.
City won the two-legged tie 5-2 after a 2-0 win in the second.
The goal came just when the match was meandering towards extra-time as the 62,000-plus capacity crowd at the Salt Lake Stadium erupted in joy.
The Serb took Blasters to the ISL playoffs three seasons on the trot. The 46-year-old was a huge hit with the Yellow Brigade's supporters.
Chhangte scored two of City three late goals in a 3-2 win at Fatorda.
The Juggernauts thus secured their first-ever ISL win over the Mariners after nine attempts, as a game of close margins kicked off amid frenetic circumstances with all three goals being netted in the first-half of this match.
One of the major takeaways for the team this season was the way the reserves stepped up to fill in the void left by the seniors.
While Goa's first goal by Noah Sadaoui was a product of a proper team effort, the other one by Brandon Fernandes was one of the most sensational solo strikes of the season.
Isak Vanlalruatfela struck the winner in the 98th minute.