While Cook admitted England had erred in selection - picking four seamers on a pitch where India's spinners claimed 19 wickets - he felt the defining moments of the game came when England failed to take chances to dismiss all three of India's centurions in the relatively early stages of their innings.
Jonny Bairstow missed a stumping opportunity off M Vijay when he had 45, Virat Kohli was put down by Adil Rashid - a difficult caught and bowled chance - on 68, and Joe Root put down Jayant Yadav at slip when he had eight. Vijay went on to score 136, Kohli made 235 and Yadav 104.
The frustration for Cook is that these things keep happening. The series against Pakistan was littered with missed opportunities - and Rashid also put down a tough chance off Kohli in Visakhapatnam when he had scored 56. He went on to make 167.
"I keep going back to the chances we missed," Cook told Star Sports. "That's why we lost this game.
"Yes, we would have liked another spinner. But with the side we had, we had opportunities to bowl India out for 400 and we just didn't take them.
"Obviously Virat played an extraordinary innings, but we had a chance to get rid of him on 60-odd. Yadav got a 100 and we had a couple of chances to get rid of him. And those are the things the game is changing on. This team, at the moment, we're not taking those chances. It's those opportunities that have cost us."
Cook also admitted England "didn't need that extra seamer" in Mumbai. Going into the match with six bowlers - two spinners and four quicks - Cook was obliged to ask Rashid and Moeen Ali to deliver more than 50 overs, while none of the seamers bowled more than 20.
"That was a mistake," he said. "It's kind of the problem when you don't have any games between Test Matches. We really wanted to see what four seamers looked like, because they are the bowlers so far on this tour who have given us the most control and our two best spinners have been Mo and Rash.
"Maybe if we'd bowled first we'd have more control with the four seamers. But clearly when you bat first, you didn't need that extra seamer.
"Whether it would have changed the game... we were in this game with the balance of that side. We had an opportunity when they were 307 for 6 to restrict India's lead. Historically, 180 is a good score here in the third innings and it's very hard to score much in the fourth innings. So we would have been in the game.
"But would have, could have isn't really good enough and that's the bottom line: we haven't been good enough to get over the line."
Cook had praise for Kohli, though: "He's in incredible form. He's having one of those series you dream of as a player and a captain. You lead from the front and you score a hell of a lot of runs and that's a huge amount of credit to him. He's clearly one of the great batsmen of our generation. And certainly in these conditions, he's very hard to bowl at when he's in this form."