England are trailing the five-match series 0-3 after losing the fourth ODI by nine wickets against India at Edgbaston here today.
"At this precise moment in time, no," said Cook when asked whether he will relinquish his ODI captaincy.
"I will be the captain of this team in the World Cup if I'm allowed to be. I don't have a say on selection but I've captained for three-and-a-half years with the goal to try to win the World Cup in Australia.
"I know that seems a bit far-fetched at the moment when we're losing games of cricket but there are a lot of really good players in that change room and if we can improve at the rate we need to improve. We've got a chance and that's what we have to believe in," he said.
England's batting collapsed once again and scored only 206 runs before they were bowled out in the 50th over of their innings.
India then chased down the target with 19.3 overs to spare with Ajinkya Rahane (106) scoring his maiden ODI century and putting up 183 runs with Shikhar Dhawan (97 not out) for the opening wicket.
"It was a tough performance to take in, to lose by nine wickets, and we were behind the game very quickly and we never got back into it," said Cook.
"When you get behind in a series, trying to turn it around especially in the one-dayers when it happens so quickly, is the toughest and most frustrating thing as captain. You know you've got to go out there and play with freedom but when you keep losing wickets it's very hard to do that," he said.
The English captain ruled out that team selection or wrong strategy were the real cause of these defeats and instead pointed out non-performance of his players as the reason.
"We don't quite know our best eleven at the moment because the results are showing we're not performing. So when that happens, you always start to doubt and that's the position we're in at the moment. We've got six months of one-day cricket to try and put that right," Cook said.
"I don't think the strategy does need to change, I just think we need to do it better. The first two games we got really good starts off the first 10 overs and the problem is none of us have gone on. Alex Hales and I in those two games, none of us went on and then today we didn't get off to a good start so tactics and strategies kind of go out of the window when you're 20-3 or when you're 90-5 after a collapse. So the top order has to score heavy runs at a good rate, it's fairly simple," he added.