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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.
Chhangte scored two of City three late goals in a 3-2 win at Fatorda.
ISL: Mohun Bagan Super Giant beat Mumbai City to lift League Shield
With 45 points from 21 games, the Mariners are trailing top-placed Mumbai City FC by two points.
City won 2-1 to take their tally to 47 points while Mohun Bagan Super Giant are second on 42 points.
Lallianzuala Chhangte opened the scoring in a 3-0 win for Mumbai City.
The AIFF disciplinary committee found a March 8 complaint to be valid. The match had ended 1-1.
Mumbai City won 4-1 to take their points tally to 39.
City and Jamshedpur played out a 1-1 draw in the Indian Super League on Friday.