"I won't be retiring from one-day cricket. I am not stupid," said Vaughan after South Africa inflicted a nine-wicket defeat on England here on Tuesday to book the last place in the semi-finals.
It is the fourth successive time that England have failed to qualify for the last four since finishing runners-up to Pakistan in the 1992 tournament in Australia.
England failed to fire in the highly-charged match at Kensington Oval which both teams needed to win to keep their World Cup dreams on track.
South Africa dismissed England for a paltry 154, with medium-pacer Andrew Hall taking a career-best 5-18, and then cruised home with captain Graeme Smith smashing a 59-ball, 89 not out in a one-sided contest.
"I know it's an area (his position) of concern and it will be an area of talk over the next few days. The most important thing is getting England back on track," said Vaughan.
"There needs to be a lot of honesty. We, as an England team, have had a very disappointing six months. We got hammered in the Champions Trophy, lost the Ashes 5-0, won the tri-series, smiled our way home on the flight, then turned up at the World Cup thinking we had a great chance of playing well.
"I firmly believed we would do a lot better than we have. To get knocked out of the World Cup in the circumstances that we have is not good enough for the talent in that dressing room."
Vaughan's dismal form with the bat continued as he fell for 17 and now has a miserable 130 in eight matches at the World Cup.
"My batting form has not been good at all in one-day cricket. I'm a very honest guy that says my position in the team is hugely in doubt because of my batting.
"But I still believe I am a very good captain, so people will have to sit down and discuss my position.
"We need to work out why it's gone wrong and work out who is the best person to lead us forward because the grass isn't always greener," said Vaughan whose injury allowed Andrew Flintoff to lead the team in Australia.
"It is not about Vaughan or (coach) Duncan Fletcher, it's about people coming up with a strategy, thinking about who is the best person to lead England forward, who is the best coach to lead England forward and if it's me and Fletch we will have to come forward and make a better strategy."
Besides Vaughan, Fletcher's position will also be under pressure after the World Cup exit but the England captain backed his coach.
"He is still an outstanding coach. I still think he has a tremendous amount to offer the English game. Only he knows how he is feeling at this moment in time. I know he will be very disappointed and hurt inside."
Vaughan said England's performance had let down the huge army of fans who had come to the Caribbean.
"It is a very sad day for English cricket, it's a horrible feeling to have walked off the park in Barbados and be booed by a lot of English supporters, rightfully so from the performance we put in.
"I fully understand why they have given us that kind of reception. It is a massive tournament. It is not a nice feeling but you have to accept it."