Shirley Henderson, 46, from Carluke, died on Thursday in the intensive care unit of Wishaw General Hospital.
She developed DVT, also known as economy class syndrome, when she travelled to Singapore in April.
She was allowed to return to the UK on medication to thin her blood and had been attending hospital for blood checks.
Her husband Alistair has criticised the clinic for failing to identify the danger she faced.
Mr Henderson said: "They said at the clinic that her blood checks were good and she didn't have to come back for three weeks.
"I believe that if she had gone back every week, then they could have picked up that her blood level was far too thin - effectively, she bled to death."
Mrs Henderson became unwell while travelling to Singapore and collapsed when she got off the plane in April.
She was immediately rushed to hospital where doctors found she had DVT.
She was allowed to fly home to Scotland one month later after taking medicine designed to thin her blood.
Blood clot
However, her condition deteriorated when she arrived back in Scotland, where she was again admitted to hospital.
Doctors believe long inactive periods in cramped spaces commonly cause a symptomless variety of DVT, but in more serious cases a blood clot can develop and travel to the heart and lungs.
The problem came to public notice following high-profile cases like that of 28-year-old Emma Christofferson, from south Wales, who died after a 20-hour flight from Australia.
She suffered a massive blood clot after sleeping for most of the journey, and collapsed and died shortly after arriving at Heathrow Airport last October.
Her case prompted calls for more information about the condition. Some airlines are now issuing advice to passengers with their tickets on how to prevent the onset of DVT.