Cook made only a single as England lost to Sri Lanka by 90 runs to trail 4-2 with one match remaining on Tuesday.
Asked if he expected to be captain when England travel down under next month, first of all for a tri-series against Australia and India, he said: "Yes.
"It's tough at the moment. I'm a better player than I'm showing at the moment, and I've just got to keep going."
The skipper has now scored 499 runs at an average of 24.95 - with only one half century - in his last 21 ODIs, during which time England have won only eight matches.
"Not scoring the runs I'd like is not a great place to be as a captain," said Cook, who has scored five ODI centuries in 91 one-day international appearances.
Four of those hundreds have been as skipper, but the most recent came against West Indies in June 2012.
"You want to lead from the front, and when it's not happening for you it is incredibly frustrating," he said.
Cook's difficult day began when he dropped key Sri Lanka batsman Kumar Sangakkara on 41 and the left-hander went on to make 112.
"Days like these don't make the job any easier," he said.
"It's probably a good job I'm off a lot of social media and in the middle of Sri Lanka at the moment where the internet is not so great."
Meanwhile, England coach Peter Moores said the situation would be assessed after the completion of the Sri Lanka series.
"It would be wrong of me as a selector and coach not to review things at the end of this series," Moores told Sky Sports.
"Alastair's in a tough patch at the moment but he's working extremely hard to get out of that."
After Tuesday's final match in Colombo, England have only four guaranteed matches in the triangular series against Australia and India next month before their World Cup campaign begins against co-hosts Australia on 14 February.
Moores also defended Eoin Morgan, who was out first ball in Pallekele on Saturday and has made only one fifty in his last 18 ODI innings.
"I think Morgan's playing well. He got a beauty today. He plays a style of cricket that aggressive and can win matches," he said.
"Australia is a place where he has performed well in the past.
"We'll try and pick a 15 for the tri-series that will be the team for the World Cup. You want your side settled by the time you get to that stage."

The club said the 25-year-old would be out for "a number of weeks".
Forrester sustained the injury in the Scottish Challenge Cup final win over Peterhead on Sunday.
Earlier this week, he signed a new contract to stay at Ibrox until 2019 after helping Rangers win the Championship.

Willie Boy O'Neill, three, and Tojo O'Neill, two, formerly of Caldon Road, were last seen on 3 August.
They are believed to be in the company of their parents, Claire Watson, 32 and 39-year-old Robert O'Neill (39).
The children were reported missing after council officials became concerned for their welfare after failing to contact the family.
Willie Boy is described as being of slim build with fair hair, whilst Tojo is stocky with fair hair.
Since being reported missing to police last week, officers have made extensive inquiries in England - where there are family connections - to trace the family.
So far, there have been no positive sightings of the children, except for the whole family being seen together within the Rivergate Shopping Centre in Irvine at 14:45 on Sunday 3 August.
Police have appealed for anyone with information about the children's whereabouts to contact them urgently.
Alastair Cook has vowed to remain England one-day captain despite losing a fourth successive one-day series.
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Rangers winger Harry Forrester will miss Sunday's Scottish Cup semi-final against Celtic after a scan revealed he has a hairline fracture of the leg.
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Police are attempting to trace two children who have been missing from the Irvine area of North Ayrshire.