Supreme Court justices ruled against Paul Lamb and Jane Nicklinson by a seven-two majority following a hearing in London.
Mr Lamb and Mrs Nicklinson, whose husband Tony died nearly two years ago, wanted the court to rule disabled people should have the right to be helped to die with dignity.
Nine justices had been asked to decide whether a prohibition on assisted suicide - outlined in the 1961 Suicide Act - was compatible with the right to respect for private and family life enshrined in the European Convention on Human Rights.
Five of the nine justices concluded the court had the "constitutional authority" to declare a general prohibition on assisted suicide was incompatible with the human right to private and family life. Two of those five said they would have made such a declaration.
Mr Lamb, from Bramley, Leeds, and Mrs Nicklinson, both 58, said those conclusions were a "positive" step in the fight for change.
He added: "I know it is going to change."
Mrs Nicklinson - from Melksham, Wiltshire, and whose husband Tony died aged 58 in August 2012 after starting the legal fight - added: "I am disappointed that we lost. But it is a very positive step. Parliament will have to discuss this."