Needing just eight to win off the final over in Nagpur on Sunday night, England were stunned by the dismissal of their star batsman Joe Root off the first ball and ultimately fell five runs short of their target.
TV replays showed that Root had got a thick inside edge onto his pads but he had no chance of challenging Indian umpire Chettithody Shamshuddin's decision as DRS is only used in test match and ODI cricket.
The same umpire also turned down a vehement lbw appeal from England bowler Chris Jordan who was convinced he had dismissed Virat Kohli during India's innings.
Replays indicated that the ball would have hit off and middle stumps but Kohli, who was on seven at the time, was reprieved and went on to score another crucial 14 runs.
England skipper Morgan admitted there was "extreme frustration" in the visitors' dressing-room after the match, saying it was time for DRS to be introduced for the game's shortest format.
"The fact it's not (available) is a concern. There is as much on the line as there is in a test or a one-day match so no reason why it shouldn't be used," Morgan told the post-match press conference.