A flat pitch had offered little throughout the five days and, although England had a sniff of victory early on the final day, India stood firm with the match finally over when they declared on 391 for nine.
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"When they got above 250-260 you felt we weren't going to win," he said.
"We had a sniff when they were only 200 ahead but the wicket won."
That it was England, and not India, who were the ones to be chasing victory was somewhat remarkable, not least after they had been 202 for seven while chasing India's first-innings total of 457.
Joe Root's 154 and 81 from last James Anderson helped England take a first-innings lead of 39, giving England hope once India were at 184 for six in their second innings.
"We dragged ourselves out of a hole," Cook said. "We had a poor session when we lost six wickets. It was an outstanding hundred from Root and with Jimmy to have got 80-something. I didn't see it coming, but thank goodness he got it."
With the game drifting towards a draw, Cook brought himself on to bowl late in the day and in only his third Test over, he took his first wicket when Ishant Sharma was nonchalantly caught by Prior down the leg side for 13.
"A few people aren't talking to me," he said. "It was a extraordinary moment for me to have more Test wickets than (bowling coach) David Saker."
But while he could enjoy a laugh, Cook and England still have serious concerns over how they can take the wickets needed to win a Test - a move which has led to the call-up of left-arm spinner Simon Kerrigan in the squad for the second Test at Lord's.
"We're seeing a lot of dry weather," Cook said. "If we get a pitch with pace and bounce that attack will be hard to bat against, but we haven't had one of those wickets so we have to have a contingency plan.
"We know we can put India under some pressure when we bat. We just need a pitch with a bit of life in it."
The hosts had just the most fleeting and improbable glimpse of opening up a run chase when India lost three wickets in the first hour of the final morning, but debutant Stuart Binny (78) emphatically restored order.
For good measure, as India closed out the inevitable on 391 for nine declared, Bhuvneshwar Kumar (63no) bagged his second half-century of the contest - and his Test career - as a lifeless surface had the final say.
England arrived here with issues over the batting form of Cook and the workload to come this summer for frontline pace bowlers James Anderson and Stuart Broad. After only five runs for Cook and 113 overs to no avail for Anderson and Broad, there is no less cause for concern.
For a few minutes of a cloudy morning, after Broad took two of three wickets to fall, there was just the outside possibility England could continue that rate of progress.
Binny put paid to that fanciful theory, however, in stands of 65 with Ravindra Jadeja for the seventh wicket and then 91 with Kumar for the eighth.