England captain Cook was given out caught behind by India skipper Mahendra Singh Dhoni on day four of the fourth Test in Nagpur despite replays showing he had made no contact with the delivery from off-spinner Ravichandran Ashwin. The opener had also been adjudged lbw in the first innings when a delivery from Ishant Sharma appeared to be missing leg stump.
India have consistently been opposed to implementing DRS in Test cricket but Morris told BBC Radio Five Live's Sportsweek programme: "We made our views pretty clear at the beginning of the series. We believe DRS improves decision-making on the field. That has got to be good for the game."
He added: "It is disappointing we are not using it in this series - and we should be. Over the last few years the DRS has really bedded into our game, has improved our game. We should be using it."
Morris hailed the impact made by Cook with the bat and as captain in his first full series as Test skipper.
He said: "Alastair, for the past 15 to 18 months, has been captain of the one-day squad and has really taken that team forward.
"The way he has gone about his business in India has been hugely impressive with the bat and as a leader. He has got the respect of the changing room. On his first major tour, he has led the team extremely well."
Morris also praised the reintegration of Kevin Pietersen after his summer fall-out following comments after the second Test with South Africa.
He said: "It has worked out really well both on and off the field. We've moved on from where we were in the summer. Kevin sat down with the players and the management team and any outstanding issues have been put to bed.
"Off the field, he has done everything we've asked of him and on the field he has made huge contributions. The innings in Mumbai was a great innings, one of the great modern Test innings by an England batsman."