Root’s position is under the spotlight after the 1-0 series defeat, which came on the back of a woeful 4-0 Ashes thrashing by Australia.
That extended England’s poor run to four successive Test series defeats.
The 31-year-old Yorkshire batsman has led England in a record 64 Tests, winning 27 games more than any other captain but lost 26, which is also more than any other skipper.
Vaughan, who captained England 51 times from 2003-08, says it is better to have him in the side without the burden of the captaincy.
“He’s taken it as far as he possibly can,” Vaughan told the BBC.
“If he rings me next week and asks for some advice I’ll be dead honest I’d tell him to step down.
“Will England be any worse off not having him as a captain? I don’t think they would, because they are going to get his runs and a senior player.”
Former England captain Andrew Strauss and Paul Collingwood are filling the roles of director of cricket and coach respectively following the departures of Ashley Giles and Chris Silverwood prior to the West Indies series.
“I wouldn’t want the new director of cricket or head coach to sack him (Root) he’s deserved the right to go on his own ground,” said Vaughan.
“During his reign I don’t think he has been helped at all.
“His first Ashes series there was the Ben Stokes incident (a late night fracas outside a Bristol bar), then we had the white-ball reset, then he’s had Covid and it’s been very difficult.”
Vaughan, however, insisted Root had fallen short as a captain as well.
“Tactically he has been poor,” said Vaughan.
“It has been a common trend under Joe he hasn’t managed to grab a game. If he does carry on he’ll really need someone who can drive the tactical side of the game with him.”
Root, however, has been adamant he wants to carry on as captain and is resolute in his belief that England are on the brink of a bright future.
“A difficult defeat to take because I really think there were a lot of positives to come from the way we played for the vast majority of this series,” Root posted on his social media channels on Tuesday.
“After a long winter, it’s time to take a break and recharge ahead of the summer, but I believe in the future of this team.”
Root did receive support from England’s record wicket-taker James Anderson who, along with fellow opening bowler Stuart Broad, was controversially omitted from the West Indies tour.
“If you get the right people in those two jobs above him then he can still do a really good job,” Anderson said.