"The frustrating thing is that every side I seem to play in for England, there's a question about my place. That's a hard place to work from."
Tuesday's nine-wicket hammering at Edgbaston was the latest of three heavy defeats and gave India the series win. Ex-players such as Graeme Swann are calling for him to step down as one-day skipper.
Cook's position as test captain came under scrutiny when India took a 1-0 lead in the test series earlier in the summer, only for England to complete a 3-1 victory.
"I went from 1-0 down to 3-1. It changes very quickly in sport. My credibility is not for me to comment on," said opening batsman Cook whose 2014 average in 13 one-day games is 29.8.
"I know I have to score more runs," said Cook. "I've done that in the past and I will in the future.
"I've had three-and-a-half years of one-day captaincy experience. We've done some really good stuff in that time, but we're having a heavy blip at the moment."
The latest heavy defeat by India came after the hosts were bowled out for only 206 in Birmingham, with the tourists chasing down their target with 117 balls to spare.
Cook took charge of the one-day international side in 2011, leading England to the top of the ODI world rankings in 2012.
But England have lost nine of their last 12 completed ODIs under Cook's captaincy against Test-playing nations.
The final game at Headingley on Friday is England's last home ODI before the World Cup in Australia and New Zealand, which begins in February.
"The players have to look at themselves and turn it around. The guys are hungry to succeed, we're just not delivering at the moment. If anyone thinks their place is safe, then they are wrong."
(Reporting By Tony Goodson)
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