"We need to perform well throughout the tour and be consistent which we failed to do last time," Dravid told reporters before his team's departure for the Caribbean for four Tests and five One-dayers.
India have lost seven of their eight Test series in the West Indies, their lone success coming in 1971 under Ajit Wadekar's captaincy.
"We have not won a Test series in the West Indies for a long time. We had chances of winning it during the last tour (in 2002), but failed to grab them. We have to concentrate on doing the basics right," said Dravid.
On their last visit to the Caribbean in 2002 under Sourav Ganguly, India won the second Test in Trinidad before losing the third and fifth to surrender the five-match series. The remaining two Tests were drawn.
The Indian captain said his team would focus on the upcoming series rather than the World Cup, to be held in the West Indies next year.
"We are not going to focus on the World Cup on this tour. There is a big buzz as the World Cup is next year, but we cannot do anything about it. We just have to focus on winning the upcoming series," he said.
"If we do well and have a few successes on this tour, it will surely help us in the World Cup."
India have done well in One-dayers under Dravid and coach Greg Chappell, winning 18 matches and losing six.
But their Test performance left a lot to be desired as they lost a series in Pakistan early this year and drew a home series against an injury-hit England side in March.
"It is just that we have done better in One-dayers, but we are trying to be a good side in both forms of the game," said Dravid.
He said the West Indies could not be underestimated despite winning just four of the 15 Test series since 2002.
"They play well at home. Their bowling attack may not have big names but it looked good when we met them in a tri-series in Sri Lanka last year," he said.
India have won just three of their 38 Tests in the West Indies.