The loss was the fourth time since 2001 when India have won a Test only to lose the next with the nine-wicket defeat in Lahore following a trend started in Zimbabwe in 2001, continued in West Indies in 2002 and then in Australia last year.
"It's an area of concern for us that needs to be addressed," Dravid told reporters. "It's disappointing to lose another Test abroad after winning the previous one."
India have not won an overseas Test series since beating Sri Lanka in 1993-94, though Dravid, who is expected to step down from the captaincy when regular skipper Saurav Ganguly returns from a back injury for the third Test in Rawalpindi, said the team was still hopeful of breaking that run.
Excerpts from the Press conference:
On the reasons for the defeat: They (Pakistan) played well over three-and-a-half days. They played better cricket than us. It is as simple as that.
On what the team could have done better: You can look back upon (a lot of areas) and do (things) differently. I wish we had batted better, got the tail out quicker, but the toss is not the only reason. We didn't bat well enough in the first session, and as you saw, the wicket was up-and-down towards the end. It would have been interesting if either team was chasing 250 on the last day. In hindsight we could have done it differently. If I knew that we would be four down at lunch, we would have done things differently. But we don't have the benefit of hindsight.
On whether his run-out in the second innings was the turning point: One run-out cannot be the turning point. It is the team that plays better that wins, and they (Pakistan) were deserving winners.
On not making runs as captain: I was looking forward to this Test. But I played a poor shot (in the first innings). I was disappointed personally, and hopefully, I will have the opportunity to correct this in Rawalpindi. And make some runs on this tour.
On Pakistan's tail wagging in the first innings: In the first innings we could have done with 75 more runs. And we could have restricted them to less. We needed 150 runs from somewhere. Shoaib Akhtar showed the character to stay at the wicket, something that is not in his nature. Credit to him.
On whether mental fatigue led to a rare occasion when India's batting failed in both innings of a Test: There was no mental fatigue, at least I hope not. We were all very keen and excited to play well here. It's very hard to point out exact reasons why we failed twice. We know we are most dangerous when we bat well and put runs on the board.
On whether umpiring decisions going against India made a difference: We were better in Multan, they were better than us here, and in both games the better team won. Umpiring is part and parcel of the game. I believe that both teams should accept what they get in terms of umpiring.
On the fact that India has won the first Test of a series and then immediately lost the next in away series: We definitely think that we have not (handled) this aspect well. We have to find solutions to that problem. I don't think complacency was a factor. It is not as if we did not try hard enough. That is something we can rule out. We have changed a lot of things over the last two-and-a-half years and hopefully this is something we can change.
On the positives India can take out of this match: Yuvraj (Singh) was brilliant. He was batting under pressure and did brilliantly for someone who is playing only his third Test. (Irfan) Pathan and (Lakshmipathy) Balaji showed great heart on what became a flat wicket on the second and third days. They ran in hard consistently. Viru (Virender Sehwag) has been fantastic and Parthiv's attitude towards the end showed guts and character. I couldn't have asked for more.
On Umar Gul's spell in the first innings: I admit (Umar) Gul was a surprise package, an inspired selection. Hats off to the young kid. He did well to put the ball in the right areas. He broke the back of our batting and was deservedly the Man of the Match.
On the fact that India won comprehensively in Multan and that Pakistan also completed their win with plenty of time to spare: It has been an evenly contested series. Neither team has had a clear advantage. Whoever executes their plans better is going to win. It will be the same in Rawalpindi.
On coming back from defeat: It's disappointing to lose - personally and as a team. I don't deny that. But character is how you pick yourself up and come back. It does hurt but you have to look ahead and stay positive.
On whether the deciding Test would be more intense and competitive: It has been intense and competitive right through. It can't get any more intense than it already has. Rawalpindi is an important game, the last of this tour.
On whether the team was affected by speculation about who would be dropped if Yuvraj Singh was to be included in the third Test: It did not affect the side. That's the beauty of the game. In this part of the world all sorts of things are discussed, in boardrooms and living rooms, but there was no talk about this in the dressing room.