England's 15-run loss to Bangladesh in Adelaide on Monday night means they can't reach the finals, regardless of their last group game against Afghanistan on Friday.
Morgan, who said that apart from disappointment his main emotion was surprise at the failed campaign, wants to remain captain.
"I haven't thought a great deal about it because this has come as a great surprise, but certainly I have enjoyed the captaincy," he said.
Moores hoped he would continue as coach but conceded it wasn't his decision. "I want to carry on, definitely," he said. "At a time like now you feel hollow inside and you feel hugely disappointed.
"So you're not going to do a lot of thinking apart from the disappointment you have got for a campaign we had a huge ambition for.
"Any analysis of anything else I will do later, not today."
Moores conceded there would be fallout from a woeful campaign of just one win, against minnows Scotland, in five games.
"I'm not going to stand here and say we all shouldn't take some responsibility, of course we should," Moores said.
"[But] there is some deeper-seated things that go with our one-day cricket ... we are behind and we have got to catch that up."
Moores said England needed to play more one-dayers against other top-notch nations.
"We prepared well. We have covered the right stuff but we haven't played well on the field, we certainly haven't put it together.
"There has been a lack of consistency but also there is no lack of passion or desire in that team."
Meanwhile, Bangladesh skipper Mashrafe Mortaza has been fined 40 per cent of his match fee, while his players received 20 per cent fines, for a slow over rate.
Mortaza will cop a one-match ban should Bangladesh commit a second slow-over offence with him as captain.
- AAP
