The title holders lost the semifinal spot to Army XI on goal difference.
Air India squandered a brilliant opportunity when Joga Singh after breaking through the rival defence failed to get past Tamil Nadu goalkeeper Udhaya Kumar in the seventh minute.
But Tamil Nadu skipper V Raja helped his side draw the first blood in the same minute.
Tamil Nadu equalised early in second half with a goal from Dhileepan in the 37th minute.
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Joga Singh scored a field goal for the airline company in the 42nd minute. Gaganpreet converted two more penalty corners in the 47th and 52nd minute to put Air India ahead 5-2 but the southern team came back with two quick goals in the 56th and 58th minute from Albert John and D Dhamu.
In another Group A match, Western Railway beat Army XI 5-3. Army men took the lead in the 16th minute through a penalty corner by Chandan Aind but Western Railway slammed in two quick goals in 21st and 25th through Amit Rohidass, who scored from a penalty corner, and Malak Singh who scored a field goal.