Juan Watterson was seeking approval to introduce a private member's bill aimed at changing Manx law.
But Members of the House of Keys voted 17 to five against the motion.
"I am disappointed," said Mr Watterson. "I thought the vote would be a lot closer than that but that is the democratic process - it is what it is and you have to respect that."
Millie Blenkinsop-French, from Douglas, who has suffered two mini strokes, said: "I am bitterly disappointed but I won't give up.
"I'm not afraid of dying, but it's how I die that worries me. It should be my choice."
The 71-year-old added: "If nothing else I will make it my business to go around and give talks. We need to learn to talk about death as well as living."
Peter Murcott, who campaigns against assisted dying, said Mr Watterson's plan goes "against Christian beliefs".
He said: "If you kill someone intentionally then in law it is murder and that is what euthanasia is."
Isle of Man politicians have rejected a call to introduce a bill to allow assisted dying.