The Kemp's ridley turtle was one of two found on beaches near Formby, Merseyside, and Cumbria's Walney Island on 22 December.
The reptile found in Merseyside died soon after, but the other was being looked after at the Lake District Coast Aquarium in Maryport.
Aquarium owner Mark Vollers said it had struggled to feed itself.
The turtles were believed to be from the Gulf of Mexico 5,000 miles (8,000 km) away and were among a small number which washed up on British and European shores last month.
Mr Vollers told BBC Cumbria: "We thought we had a 50/50 chance, which would've improved if it had started feeding.
"It was getting some sustenance in other ways but not really enough to recover.
"We were following a strict agreed protocol arrived at after consultation with vets here and in other countries - people who have experience of this species of turtle."
The turtle, possibly aged about 20, is now with a specialist vet who will determine the cause of death.
Source: World Wide Fund for Nature (WWF)

Some Australian states already have "no jab, no play" laws, but PM Malcolm Turnbull is calling for nationwide legislation.
Health groups have supported the push, arguing parents and the community have an obligation to protect children.
An Australian Child Health Poll survey of nearly 2,000 parents showed 5% of children were not fully vaccinated.
Mr Turnbull said more needed to be done, citing the case of a baby who died from whooping cough.
"This is not a theoretical exercise - this is life and death," Mr Turnbull said.
"If a parent says, 'I'm not going to vaccinate my child,' they are not simply putting their child at risk, they are putting everybody else's children at risk too."
Vaccinating children is not a legal requirement in Australia, but failing to do so makes parents ineligible for childcare rebates.
Three Australian states - Queensland, New South Wales and Victoria - already require children to be immunised, or be on an approved catch-up programme, to enrol in childcare centres.
Australian Medical Association president Michael Gannon said children were more susceptible to infections.
"If you, as a parent, expect the community to support you by either welfare payments or access to care, then you need to do your bit to contribute to that community by protecting other children," he told Fairfax Media.
The so-called "anti-vax" movement believes vaccinations may cause medical conditions such as autism, but overwhelming scientific research suggests this is not the case.
Vaccines can cause adverse reactions in a small number of people, like many medicines, but the accepted science is that the benefits far outweigh the risks.
Widespread vaccination also reduces the risk of infection to those who, for medical reasons, may not be able to receive the vaccine themselves.
So-called "herd immunity" is an important part of public health programmes. It stops the spread of disease by preventing an infection from moving among most people - the ones who have been vaccinated. And so it protects those few without the vaccine.
But as the numbers of those without protection rises, so to does the risk to each of them - something which happened alongside the first death from measles in the United States in 12 years.

This is the first time that an English side of any age has been able to call themselves football world champions since England won the World Cup in 1966.
The Under-20 World Cup is the biggest global tournament in youth football and has been an important launch-pad for a lot of big names in football.
Lionel Messi, Luis Figo, and Paul Pogba were all been part of winning sides in the tournament in the past.
So could this team hold the next generation of English football stars?
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Congratulations England you did very well.
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A turtle, thought to be from the Gulf of Mexico, that washed up on a Cumbrian beach has died.
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Unvaccinated children would be banned from childcare centres and preschools under an Australian government plan.
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It's a huge day for English football, as England's under-20s beat Venezuela to take victory in the Fifa Under-20 World Cup.