England were denied a victory as India held out on the final evening of the first Test on 172-6 but Cook hailed the “bloody hard work” his side had put in and congratulated them on an admirably sustained and skilful effort.
England will travel to Vizag on the back of four individual hundreds, Cook’s 30th in Tests coming in their second-innings 260-3 declared, and seven wickets from Yorkshire leg-spinner Adil Rashid.
After Cook’s 130 and 82 on debut from his new teenage opening partner Haseeb Hameed, in a stand of 180, he was able to set India 310 to win in a minimum 49 overs.
At 71-4 with almost two hours left to play they looked in big trouble, only for home captain Virat Kohli to save the day with an unbeaten 49.
Cook appeared exhausted at his post-match press conference, but summoned the energy to praise his team for moving on so evidently from the shock defeat to Bangladesh in Dhaka which prefaced this campaign.
“It was a brilliant performance all round – especially from our three spinners,” he said.
“No one was talking of us having a chance in this series, but the way we played showed we’re in there.”
England’s next task is to recover in time for the start of the second Test on Thursday.
“I’m feeling fairly jaded now, and I think the lads are,” added Cook.
“Doing 160 overs in the dirt in the first innings is fairly brutal ... it’s been bloody hard work, I can tell you that. I think we put everything on the line there.”
Hameed received particular mention. The youngster marked his debut by sharing with Cook England’s highest-ever opening stand in India.
“He’s an unbelievable player,” said the captain. “He was pushing me close to retirement when we walked off yesterday – a 19-year-old not only out-batted me but scored quicker and made it look easier.
“He’s a find, isn’t he?.”
“ We said before the game we had no doubt he could play ... he certainly can play.”
So too can Stokes, who proved with his first-innings hundred that his batting can be effective in these conditions.
“He’s our golden player,” said Cook.
“He balances the side, allows us to play three seamers and three spinners.
“Turning wickets were probably his last challenge. He’s worked incredibly hard, and he’s getting rewards for it. He’s a brilliant player.”
As England’s all-time record run-scorer, Cook falls into the same category – but he spoke modestly after his fifth century in India, more than any other visiting batsman in history.
“At the top of the order, if you get in ... get through the first 30 or 40 balls, there are big scores to be had here.
“It’s our responsibility to do that, and luckily my record here is okay.”
Cook spent less than a day with his new-born youngest daughter before flying out to lead his country, and it seems he made a pact with himself to justify the itinerary.
“Yes, I’ve sacrificed a bit to come out here,” he admitted.
“It’s never easy, and you want to try to make it worthwhile and score a few runs to say it’s worth it. When you’ve seen your daughter for 18 hours ... it’s nice that you’ve scored a few runs.”
An opening draw was not his preferred reward, of course.
Kohli, by contrast, appeared understandably relieved with the outcome.
“At least we know how to draw games now!” he said, of the world’s number one team who had won 12 of their last 13 home Tests.
“Maybe we will have this situation again. Maybe we will have to apply ourselves again and show character.”
Whatever the requirements, England may not be surprised to hear the conditions of Rajkot are unlikely to prevail elsewhere.
“It was a challenging situation, but one I thought we countered really well,” added Kohli.
“I was quite surprised to see that much grass (on the pitch) ... that should not have been the case.”