The UN Security Council resolution aimed at paving a path to justice in the conflict was backed by 58 countries, including the UK.
But Russia and China used their right of veto to halt action against all perpetrators of war crimes in the crisis, which is in its fourth year. Mr Hague said he was "appalled" by the move and added: "This was an opportunity for the world to stand up for justice for the Syrian people. Russia and China's actions in preventing this are indefensible.
"Russia and China are isolated on this issue and they will have to justify to the international community and the Syrian people, why they are continuing to shield those responsible for the most horrific atrocities from justice.
"These include organised use of torture and sexual violence, indiscriminate attacks on civilian populations, the deliberate withholding of humanitarian aid from those starving to death, and the sickening use of chemical weapons against innocent people."
The French-drafted resolution had overwhelming backing from the international community, including 13 members of the Security Council, 65 co-sponsors and more than 100 NGOs worldwide as well as the Syrian National Coalition.
Mr Hague also said the UK would intensify its efforts to ensure those responsible for atrocities faced justice.
Russia and China have used their veto four times to prevent action.