Cook, having won his first match as Andrew Strauss' ODI successor batting first at The Oval, won the toss and opted to allow the tourists to set a target.
Driven by Mahela Jayawardene's classy 144 - his 15th and biggest century in the format - as well as impressive contributions from Kumar Sangakkara (69) and Angelo Mathews (46no), Sri Lanka racked up 309 for five.
That left England needing to make their highest-ever successful chase to go 2-0 up with three matches to play and they could only muster 240 all out.
"We fancied chasing, it's quite a hard ground to defend and a lot of edges can fly downhill," he said. "That was part of the reasoning to chase. Maybe in hindsight we got it wrong, but the crux of the matter is our skills. The toss didn't make that much difference, our skills let us down at times."
Cook, leading a losing side for the first time in five attempts in the 50-over game, also bemoaned the lack of a player with the sticking power of man-of-the-match Jayawardene.
"All of the top six got in but none of us did a Mahela to get us close to their score," he added.
"The positive is that we all got in and got a score but the negative is that none of us went on to get that match-winning hundred.
"I think Mahela did take risks but he executed them better than us."
Cook also defended Jade Dernbach, who was involved in a brief spat with Jayawardene when the batsman complained the Surrey man attempted to trip him as he completed a run.
Television replays were inconclusive but Cook was happy Dernbach did not shrink from the confrontation.
"I enjoyed it," said Cook.
"That's the passion you need to play cricket with. The big thing is to make sure he made sure he concentrated on the next ball and I think he did that very well.
"You have to have that passion and pride to play for England. When certain moments like that flare up it's important you don't have people taking a backward step."
Sri Lanka captain Tillakaratne Dilshan was pleased to square the series and was happy Cook opted to bowl first.
"We wanted to bat first. It was a good wicket, and we wanted to get some runs and put the pressure on the chasing side," said the opener, who was grateful to his middle order after foolishly running himself out for nine to give England a good start in the field.
"We stuck to our plan, got to 300 - and the bowlers then did a great job.
"We had a long discussion, senior players and the batting unit, about how to bat long in 50 overs - and that's how we got 300."
Having started the series at The Oval, the sides will now return to the capital for Sunday's encounter at Lord's.