Lanre Haastrup and Takesha Thomas say the European Court of Human Rights (ECHR) in Strasbourg, France, has "decided to abandon justice" when considering their son Isaiah's case.
The couple had asked the ECHR to intervene after losing two legal battles in England.
An ECHR spokesman on Tuesday said three judges had examined issues and declared the couple's application "inadmissible".
Mr Haastrup on Wednesday said judges had not listened to arguments.
A High Court judge has given doctors permission to provide only palliative care to Isaiah against the wishes of Mr Haastrup and Miss Thomas.
Mr Justice MacDonald analysed evidence at hearings in the Family Division of the High Court in January.
Specialists at King's College Hospital in London had said providing further intensive care treatment was futile and not in Isaiah's best interests.
Mr Haastrup and Miss Thomas, who are both in their 30s and from Peckham, south-east London, subsequently failed to persuade Court of Appeal judges to overturn Mr Justice MacDonald's decision.
Miss Thomas told a private trial in January: "I am a Pentecostal Christian. "For me, I don't think it is right to say who should live or who should die.
"If God wants to take the person, He will."
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