Moores, handed a second stint as head coach last April, has come under intense fire since England's defeat by Bangladesh on Monday condemned them to an early return from the World Cup.
Vaughan believes Moores' talents have been wasted.
"Moores was at his best working with the Lions (development team) many years ago," Vaughan said in the Daily Telegraph.
"The job of England coach has become about man management, helping with tactics and picking the right team.
"At international level you do not have time to coach.
"What is the best thing for English cricket going forward? I believe it is time to remover Peter Moores from his current position and put him in a job where he can have the biggest impact on English cricket."
"I always say the best coach works with kids and development programmes between the age of 15 and 20."
Vaughan said England's conservative approach to the one-day game had resulted in them being left behind by the likes of Australia, New Zealand, Sri Lanka and India, while even Ireland, Vaughan said, were playing better one-day cricket.
"England started the tournament by picking a Test match batting line-up for one-day cricket ," Vaughan said.
"(Managing director) Paul Downton said last night England needed more players appearing in Twenty20 leagues around the world to gain experience.
"Well, Alex Hales has been doing that but England did not pick him. Ravi Bopara, Michael Carberry, Luke Wright, Ben Stokes and Jason Roy, they all played Big Bash cricket but were ignored. England should have looked at these guys last year.
"You do not need five gears any more, you need eight.
"England do not get the fact that you need four Jos Buttlers, not one. You need four or five who have the ability to strike it at a rate of 120 per 100 balls."
Vaughan said the World Cup had been a wasted opportunity for England to change tack.
"I felt they had a free hand here, with no expectation of success," he said. "They had the chance to play expansive cricket and press "G" for gamble. Instead they played the safest, and most timid way."
(This story has been refiled to fix typo in paragraph nine)
(Reporting by Martyn Herman; editing by Sudipto Ganguly)
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