England captain Alastair Cook admits his side has more “questions then answers” after a 3-1 one-day international series defeat by India.

England did at least spare themselves the embarrassment of a whitewash by the world champions with a 41-run victory at Headingley on Friday.

Joe Root’s career-best 113 on his Yorkshire home ground was the backbone of England’s total of seven for 294, which at last gave their long-suffering bowlers a target they could be expected to defend.

And, after James Anderson took two early wickets, that is exactly what they did despite the dashing strokeplay of Ravindra Jadeja (87) and Ambati Rayudu (53).

It was a win England, and especially embattled skipper Cook, desperately needed.

Cook has spent much of this season answering questions about his future as England captain.

Several former England skippers called on him to quit during the preceding Test series with India, only for Cook to lead his side to a 3-1 series win.

But the likes of Michael Vaughan have now turned their attention to Cook’s one-day form, arguing the orthodox left-handed opener is ill-suited to the white ball game and the wrong man to lead England at the World Cup in Australia and New Zealand in six months’ time.

England have a diet of only limited overs cricket between now and the World Cup, starting with a seven-match ODI tour of Sri Lanka – who triumphed in both Test and one-day series action in the early part of this English season.

Asked if he had been told if he would be in charge for the Sri Lanka tour, Cook said Friday: “No, I haven’t.”

England came into this match on the back of a nine-wicket hammering at Edgbaston on Tuesday.

Reflecting on the change between games, Cook said: “We did a lot of things very well, and a lot of things we know we had to do and haven’t been doing in previous games – like one of those guys, top four or five going on and getting a big score, and then the others can support him.

“Rooty obviously was the difference. It was a fantastic hundred … to score a run-a-ball on that wicket. You saw a lot of the other guys struggle to do that.

“If we do that, we’re a tough side to beat.”

But England have still to nail down their first-choice ODI team and Cook said: “Unfortunately, this series has probably shown up a few more questions than answers – and we’re going to have to go away and think about it quite hard.”

But he insisted England had it in them to become markedly more proficient at 50 overs per side cricket between now and the start of the World Cup.

“The big improvement I think we can make is quite scary, and that’s what we’ve got to get our heads round now as players and work our nuts off to improve,” Cook said.

As for his own future, the 29-year-old Cook uttered a familiar refrain.

“There hasn’t been a press conference I’ve been in all summer when someone hasn’t mentioned my future as captain … and I always give the (same) answer – while I still want to do the job and believe I can, then I’ll carry on doing it.

“If they don’t want me to, then I’ll take it on the chin.

“The bottom line is we have lost a series,” said Cook, who this season has found himself working alongside recalled England coach Peter Moores.

This has been a gruelling season and Cook’s admission he was a weary man was entirely understandable.

“I feel tired,” he said.

“When we’ve played well, we’ve played really well – and when we’ve played badly, we’ve played pretty badly as well”.