England's chances of qualifying for the semi-finals received a significant blow as a result of the 20-run defeat, with Morgan accepting's his side's batting was "not good enough to win the game."
But Morgan refused to single out Moeen Ali, who was caught on the long-off boundary with 63 required from 70 balls, for blame. Instead he suggested the entire batting line-up should take responsibility.
WATCH on Hotstar (India only) - Stokes' unbeaten 82
"Partnerships are very important and we struggled to get any partnerships going," Morgan said. "We had a couple of individual innings but that's not good enough to win a game.
"I don't think Moeen's wicket was the turning point. There were quite a few wickets which were turning points. You've got guys coming in at No. 6 who average 40 and at No. 7 who average 30. We bat all the way down. So every single one is significant as every single one could establish a partnership that could win the game.
"There were a couple of challenges which presented themselves with the wicket. We didn't overcome them. We didn't deserve to win today's game."
Jos Buttler, England's vice-captain, agreed. But he also praised Sri Lanka's Lasith Malinga, who was named Man of the Match for his four wickets, and went on to suggest that England may have missed the injured Jason Roy.
"I think we lacked energy with the bat," he said. "We were a little bit passive as a group with the bat. And we haven't been for a long time so that, so that is the most frustrating thing.
"As a group we didn't have that intensity today. Obviously Jason is a guy who naturally gives us that but we can all do that from No. 1 to No. 11, so that is the most disappointing thing. We have played in a certain way for a long period of time and we went away from that today.
"Malinga is different. And we didn't counter him as well as we could today. But you do have to give credit to a fantastic bowler."
Despite the result, Morgan and Buttler expressed confidence in England's ability to quality for the semi-finals.
"The message is quite simple," Morgan said. "We need to do the basics of how we play well. We need to go back to the process that's made us a strong side.
"When we're beaten we tend to come back quite strong. We resort to aggressive, smart, positive cricket. So let's hope that the case when we play Australia at Lord's on Tuesday. There's no reason we why belief should not still be strong."
"That game will bring lots of intensity," Buttler said. "England and Australia games are big games and it's at a fantastic ground. This will hurt for a few days, but then we will get ready for the next game."