England slumped to defeat after the India side bowled out the visitors on 174 runs.
"Fair play to India, they outskilled us today in all three departments," Cook said.
"It was a tough time for us and we're going to have to learn from this. That's the beauty of a five-match series, you have four other chances.
"We're going to have to analyse where we went wrong and hopefully put in a better performance in a few days' time."
The visitors will try to draw level with India in the second one-day international on Monday.