They have called for better access to specialist nurses and therapists.
The Scottish government said its health strategy had helped cut mortality rates among heart and stroke patients by 40%.
The charity surveyed more than 1,160 people with the conditions and found two-thirds wanted more access to support services.
'Current services'It found significant regional variations in the rehabilitation services across Scotland.
According to the latest figures there are about 230,000 people in Scotland living with coronary heart disease, 488,000 living with chronic chest conditions and 124,000 living with the impact of a stroke.
The charity said ministers needed to invest in physiotherapists, occupational therapists and speech and language therapists to match demand.
Jane-Claire Judson, chief executive of the charity, said: "Opportunities are being missed to support people to live life to the full and current services need to rise to the challenge.
"That's why we are urging the Scottish government to commit to and invest in establishing a universal 'right to rehab' so everyone affected by these conditions can rebuild their lives.
"That means ending the variation in access to NHS rehabilitation services across the country, joining them up with community groups, investing in the right staff and making sure that everyone has access to a specialist nurse for as long as they need them."
'Patients' rights'A Scottish government spokeswoman said ministers wanted everyone to receive the best possible care from the NHS.(Not results)
She added: "Our strategy for tackling strokes and heart disease is delivering important improvements, with mortality rates reducing by around 40% for both stroke and coronary heart disease over the last 10 years.
"Pulmonary rehabilitation is already a key recommendation in our national clinical guidelines. We expect NHS boards to provide high quality care that is safe, effective, person-centred and respects patients' rights."