Having set West Indies a target of 269, India won the fourth and final Test at Sabina Park by 49 runs to win the series 1-0 and clinch a series victory in the Caribbean for the first time in 49 years.
"We played the better cricket throughout the series, and if we had had another 90 overs in Lucia, we would have probably won 2-0," he said. "We were one wicket away from winning in Antigua and three wickets away from winning in St. Lucia.
"We had our backs to the wall in St. Kitts, but never looked like losing on the last day. Dravid hailed the team effort that led to India's series triumph, despite tense draws in the first three Tests.
"We played the better cricket right from the first Test after the first two days," he said. "It's sort of nice that it all bore fruit in the end and we won the series.
"Everyone contributed at various stages -- Wasim Jaffer's 200 helped us fight back in Antigua, V.V.S. Laxman's 100 helped us save the Test in St. Kitts, Virender Sehwag's 180 almost won us the game in St Lucia. Then there was Kaif's undefeated 148 in St Lucia.
"Our spinners were brilliant right throughout. I have seen improvement in some areas, and we need to improve in other areas, it's never the finished article there is always scope for improvement."
One area of his team's performance that pleased Dravid the most was the fast bowling department.
"In the 10 years I played international cricket, I've seen Javagal Srinath and Venkatesh Prasad bowl well throughout the series in England in 1996," he said.
"This seam attack bowled well throughout this series. I have seen some fine spells in my career for India, but this is the best I have seen throughout a series since 1996.
"They are young and inexperienced, and yet they did it. Munaf Patel and Shantha Sreesanth played most of the games here, Vikram Singh also did well, and Irfan Pathan did well when he played.
He added: "None of the great fast bowlers were great after six or seven Test matches, it takes time and experience to get better in Test cricket. Unfortunately, expectations are too much.
"Unfortunately people look at who is not here, rather than looking at the people who are here, and admiring the work done by people who are part of the team.
"That's how you are going to inspire young kids, by talking about the people here."
Dravid was named man-of-the-match for his knocks of 81 and 68 in the final Test that made him an easy choice for the man-of-the-series award.