"The best team won. India's batsmen applied themselves better and they've had two spinners who have bowled well, while their seamers also bowled better than ours. History shows they're a tough nut to crack in their own conditions."
Pujara, opening in place of the absent Gautam Gambhir, added 41 to his
first-innings double century
as he and Sehwag raced towards their modest target.
Sehwag was well held by Kevin Pietersen at long-on off Graeme Swann, leaving Virat Kohli to drive Swann down the ground and seal England's seventh loss in 12 Tests this year.
The home side fully deserved their lead in the four-match series, having had the better of all but two sessions in the match, while England must improve in all departments when the second Test in Mumbai begins on Friday.
Between them, the captain and wicketkeeper scored 356 runs in the match, while the rest of England's frontline top seven - Pietersen, Nick Compton, Jonathan Trott, Ian Bell and Samit Patel - managed only 114.
The visitors can at least take heart from the way Cook and Prior dealt with India's slow bowlers in the second innings - Ravichandran Ashwin went 54 overs without taking a wicket - but 13 England wickets in the match fell to spin.
That fact seems to suggest that England's selection of only one frontline spinner in Swann was a mistake, while the pace trio of James Anderson, Tim Bresnan and Stuart Broad failed to find any of the reverse swing exploited by Indian pair Zaheer Khan and Umesh Yadav.
Cook's men can justifiably argue that their bowlers created chances - four catches were missed on a first day when India racked up 323-4 - but this highlights that fielding is another area that requires improvement.
One enforced change will be made, with Bell returning home for the birth of his child, while left-arm spinner Monty Panesar and pace bowler Steven Finn - if fully recovered from a thigh injury - could come into the reckoning.
England in Asia in 2012
1st Test v Pakistan, Dubai -
lost by 10 wickets
2nd Test v Pakistan, Abu Dhabi -
lost by 72 runs
3rd Test v Pakistan, Dubai -
lost by 71 runs
1st Test v Sri Lanka, Galle -
lost by 75 runs
2nd Test v Sri Lanka, Colombo -
won by eight wickets
1st Test v India, Ahmedabad -
lost by nine wickets
Whatever tweaks England make to their attack, this match was lost by their first-innings batting.
Cook and Prior saved them from an innings defeat on the fourth day and needed to do the bulk of the work on day five if the tourists were to avoid defeat.
They survived the first half an hour, only for Prior to miss out on a deserved century when, playing back, he tamely patted a return catch to left-armer Ojha.
Cook had defied India for more than four sessions on his way to the highest score by an England batsman following on, but his resistance was broken four overs after Prior fell by one that turned and kept low.
England's demise was only a matter of time, especially with Broad offering a leading edge back to Yadav.
The counter-attacking Swann was bowled attempting to reverse-sweep Ashwin, before Bresnan drove Zaheer to cover.
We are using archive pictures for this Test because several photo agencies, including Getty Images, have been barred from the ground following a dispute with the Board of Control for Cricket in India, while other agencies have withdrawn their photographers in protest.
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