India, runners-up in the last edition, crashed out in the Caribbean last week after losing two out of three group matches, to Bangladesh and former champions Sri Lanka.
Irate fans in the cricket-crazy country have demanded the axe fall on Dravid and coach Greg Chappell.
"He is an experienced campaigner and has all the leadership qualities," Vengsarkar told national daily Times of India on Wednesday.
Vengsarkar recalled former Australia captain Richie Benaud's comments on the role of the captain: "Captaincy is 90 percent luck and 10 percent ability."
"He (Dravid) has done quite well thus far. After all, as they say, a captain is only as good as his team."
Vengsarkar said the defeat to Bangladesh was a one-off.
"I feel Bangladesh played its best cricket in that match. I am positive if India plays Bangladesh in the future, it will win nine out of 10 matches.
"But nobody knows what will happen in that one match. That's the uncertainty of cricket. Whatever the Bangladeshis did in that match clicked."
The Indian cricket board is to analyse the national team's World Cup performance at a meeting next week.
The team, winners in 1983, had been touted as one of the favourites and were expected to get to the semi-finals at least.
The seven-week World Cup, the first to be played in the Caribbean, culminates in the Barbados final on April 28.
