"If you took Virat's runs out of the game -- I know you can't do that -- but we have put their batters under a lot of pressure," Cook said at the post match press conference.
Kohli followed up his first innings 167 with another 81 in the second essay to set a herculean 405-run target for England and they were bundled out for 158 in 97.3 overs with India taking eight wickets in a little over one session.
"What's giving me belief is over 10 days of cricket we have competed very well in India in their conditions. Yes we have lost by a big margin but the margin of runs is different. We could have played more aggressively and lost by 150 runs or so. But we went that way," Cook insisted.
Counting on the positives before going into the third Test in Mohali, Cook said: "Adil Rashid has been excellent in these two games, a real step up for him. Ali bowled really well. Jimmy (James Anderson) is good on his comeback. So a lot of good things. We have got to put the whole game together to beat India. If we can get ahead of them in Mohali, then we can put pressure on them."
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"It was a massive toss to lose but in certain periods of game we played some good cricket. We can all agree it was a good toss to win. Anyone could see that. It's a disappointing loss but we can get ahead of the game then we can put India under pressure. We just got to do that right. We are still very much in the series. A couple of good tosses will help that, there's no doubt about that," said Cook.
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On Stuart Broad availability for Mohali, Cook said it would be a "risk".
"I think it depends on how that injury settles. I think he was in a lot more pain than people know and showed a hell of a lot of character. We don't know enough about the injury yet because it's quite an unusual one and you're speaking to the wrong person about it. How much damage you can actually do to it, we'll know in the next 24 hours, 48 hours. But yes, if he plays, it will be a big risk."
"I think he does. Certainly something that the selectors will have a look at. It's hard cricket in your first few games. The difference, I think, is probably quite stark, I think from playing in Northamptonshire to playing here, suddenly every innings is scrutinised. That's the nature of the beast," he said as the youngster had scores of 13, 5, 0 in the last three innings.
However, Cook backed him, saying: "...Whether it's a technical flaw or not, people are aware of it and there is no doubt it affects guys.
England have another injury concern in Zafar Ansari as the left-arm spinner had a back spasm and did not bowl in India's second innings.