England, chasing Bangladesh's 275 for seven in a match they had to win to remain in the tournament, were shot out for 260 in the penultimate over in the day-night match.
But Morgan, struggling with his own batting form and dismissed for zero in the key game, said he was extremely disappointed at the team's early exit.
"Ultimately it's come down to the way we've performed and today was another example of us not performing or putting together a game of cricket," he said.
"You need guys scoring runs, weight of runs, you need guys threatening with the ball or building pressure. We have not done that consistently."
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Morgan, parachuted in as full-time England one-day captain shortly before the World Cup after Test skipper Alastair Cook was axed from the squad, said he still enjoyed leading the team and wanted to continue playing.
"I certainly want to play one-day cricket," he said. "I am still inspired to play Test cricket. The captaincy is something I've enjoyed.
Morgan, usually a fluent left-handed batsman, admitted his form had been poor throughout the tournament.
"My form has not been great since the end of our summer for a number of reasons. Today I hit the ball and if it had been a couple of yards on either side of the fielder it would have been a four or six."
Meanwhile, Morgan rubbished suggestions England lacked one-day players of sufficient quality.
"I think the players are good enough," he said. "Guys have put in individual performances, but they have not been consistently good enough to make it a team performance.
England, who have never won the World Cup despite being finalists in 1979, 1987 and 1992, will return home after their closing 'dead' pool match against Afghanistan in Sydney on Friday.