Dwayne Bravo bowled Yuvraj Singh with the third-last ball of the match at Sabina Park to hand West Indies a heart-stopping victory that levelled the five-match series at 1-1, after India had won the first ODI by five wickets with one ball to spare on Thursday.
Chasing a modest 199 to win, India needed 11 runs off the last over with the last pair of Yuvraj and Munaf Patel at the crease.
The two batsmen scrambled a single off the first delivery, and Yuvraj collected two successive boundaries to put India within touching distance.
Yuvraj however, failed to finish the game off, when Bravo bowled him with a slower delivery with the next ball to spark massive celebrations around the ground.
"At one stage, we did not look like we would have gotten this close because we were struggling at one stage," Dravid told reporters after the match.
"It does hurt to lose, but we have to accept these things. We are going to lose a few games, but we have to pick ourselves up, and go into the next game and do better. We have done really well so far, so there is no reason to panic because we lost.
"I do not think it is totally disheartening for anyone in the dressing room. The guys know we can do better and there are areas in which we can get tighter and keep improving. This has been our goal all the time and it will be something that we'll try to keep doing."
Although Yuvraj failed to complete the job, Dravid described the left-hander's innings as one of the finest he had seen from an Indian batsman when the side was chasing a target under pressure.
"He was just a bit unlucky in the end of what could have been a great innings," Dravid said on Sunday.
"He has played so many good innings lately, it is hard to categorise them. He has just been batting superbly and has taken his batting to another level. In this match, we saw a really exceptional innings, and it's just a pity he could not finish the job.
"The quality of the innings deserved him to finish the job, but it happens. This is part of the game, and Bravo bowled a good ball, and considering the circumstances it was a perfect yorker."
The defeat ended a record sequence for India of 17 successive ODI victories when chasing a target.
"We have been chasing really well in ODIs of late, but we had to lose one at some stage," Dravid said.
"It was a target we should have chased successfully, but we ended up not chasing well because we did not bat very well. There was no complacency. A target of 199 was reachable on that pitch, and once we faced 50 overs, we should have achieved the target.
"We lost wickets early, but there was no feeling of complacency. We did not relax at any stage. It's just that we did not play very many good shots in the middle of the innings."
The third ODI will be played on Tuesday at Warner Park in Basseterre, St. Kitts, which will be staging its first ODI, and the series concludes on Friday and Sunday at Port of Spain's Queen's Park Oval.
The ODIs will be followed by a four-Test series with matches at St. John's, Gros Islet, Basseterre which will also stage a Test for the first time, and Kingston.