Sunday saw England captain Alastair Cook suggest that the team's prospects for the tournament in Australia and New Zealand were "very good".
But former England off-spinner Swann was far more pessimistic.
Swann, speaking to BBC Radio's Test Match Special as rain washed out the first one-day international against world champions India in Bristol without a ball bowled on Monday, insisted England were "so far behind other teams" in their approach to the limited-overs game.
Opening batsman Cook's position in the one-day side has been called into question, with many pundits arguing his orthodox approach, while well-suited to Test cricket, has increasingly little place in a one-day context where big hitters dominate at the top of the order.
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"I love Cooky totally, but I do not think he should be bothering playing one-day cricket any more," said the 35-year-old Swann, who played 60 Tests and 79 ODIs for England before retiring during the team's 5-0 Ashes thrashing in Australia.
If the rain had held off in Bristol, England would have given an ODI debut to dynamic Nottinghamshire opener Alex Hales.
The 25-year-old scored England's first Twenty20 international century when he made 116 not out from 64 balls against Sri Lanka at the World Twenty20 in March.
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Swann played in the last World Cup in 2011, where England bowed out with a 10-wicket defeat by Sri Lanka in the quarter-finals in Colombo.