Paceman Stuart Broad was also sidelined for the entire series due to the
he suffered during the Ashes series.
However, apart from Bresnan all of those names are expected to be fit for the tournament, which starts on 19 February and will be jointly hosted by India, Sri Lanka and Bangladesh.
England will open their World Cup campaign against Holland on 22 February without Morgan, who did not feel that the injury to his middle finger on his left hand was anything to worry about at first.
"He injured it in that Adelaide game and didn't think it was serious but it got worse the more he played and practised," added Flower.
"The pain grew worse and therefore the medical team got onto it."
The left-hander is generally regarded as one England's better limited-overs batsmen, however, he did not have the best one-day series in Australia, scoring only 106 runs in six innings, with a top score of 30 as England slumped to a 6-1 defeat.
The 24-year-old has played 61 ODIs, scoring 1,904 runs at an average of 38.08, and at an impressive strike-rate of 81.19, including four centuries.
[Ravi Bopara] is going to be a worthy addition to our squad
England skipper Andrew Strauss
But Flower insists England's World Cup chances have not been diminished by his withdrawal.
"No-one is irreplaceable," said the 42-year-old. "Ravi Bopara is a very talented and exciting player.
"He will also bring a bit of medium-pace bowling to help out the captain. We're confident the 15 players we've got out there will gel."
Bopara has been in the West Indies with the England Lions but will fly home to join the squad before they travel to sub-continent on 12 February.
The Essex all-rounder has made 54 ODI appearances for England, scoring 1,140 runs at 28.50 with a strike-rate of 73.45, although his top score is 60. With the ball, he has taken 10 wickets at a little over 33 apiece.
"He is going to be a worthy addition to our squad," said England captain Andrew Strauss.
"He hasn't had a chance to play for us recently and we like what he can bring to the game. His bowling and his batting, his ability to clear the ropes in the middle overs."
Strauss went on to admit that the injuries suffered by England had not helped during the one-day series against Australia.
"Having a settled bowling unit has been the basis of our ODI success over the last 18 months and we certainly missed having that in Australia," he stated.
"We believe that when they are all fit our bowling unit is a match for anyone in the world."
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