No Healthcare Subsidies for Foreign Diplomats Act of 2014 - Amends the Internal Revenue Code to deny a tax credit for the cost of health insurance premiums and health insurance cost-sharing reductions under the Patient Protection and Affordable Care Act to foreign diplomats. Requires the Secretary of State to notify all foreign missions in the United States, permanent missions to the United Nations, and the United Nations Secretariat that health insurance premium tax credits and cost-sharing reductions are not available for their foreign personnel with nonimmigrant status under the Immigration and Nationality Act.