The tourists' slow bowlers proved highly influential once again on Saturday as MS Dhoni's men followed up their 133-run victory in Cardiff with a convincing six-wicket triumph at Trent Bridge.
England, who were bowled out for 227 despite an opening stand of 82 between captain Cook and Alex Hales, must now win next week's remaining matches at Edgbaston and Headingley to avoid a series defeat.
Cook is aware such a feat will only be achieved if his side make a better job of combating India's spinners, who accounted for six of England's top seven batsmen in their latest success.
"[Spin] is something we need to keep trying to work on, we're not doing it right," Cook told Sky Sports.
"I think the ball spinned [sic] off the pitch more in the morning than it did in the afternoon but I still don't think it was a 230 pitch.
"We need to keep working because if we don't we will keep not getting enough [runs].
"I didn't think Trent Bridge would spin as much as it did but you have to adjust to that.
"The bottom line is we didn't play very well with the bat.
"There are some good players there, who are not showing it. It's something we need to change around."
Frontline spinners Ravichandran Ashwin and Ravindra Jadeja returned respective figures of 3-39 and 1-38 as England struggled to score freely.
Yet India skipper Dhoni was keen to highlight the efforts of part-timers Suresh Raina and Ambati Rayudu, who accounted for England's openers after seamer Mohit Sharma had picked up an injury.
Rayudu, called up in place of Rohit Sharma (fractured finger), claimed his first international wicket by having Cook stumped and went on to underpin India's successful chase with 64 not out.
"The spinners did it for us," said Dhoni.
"Ashwin and Jadeja did really well, but it was also Suresh's spell after Mohit's injury.
"I never thought it would spin and in the back of my mind I was wary the ball wouldn't do a lot.
"Rayudu did very well; we are still looking for a number four batsman and there are a few out there."