Mr Hague was speaking after talks at the Foreign Office in London with John Kerry at the end of the US Secretary of State's whirlwind tour of Europe to garner support for punitive action against the regime of President Bashar Assad following its use of chemical weapons on civilians in a suburb of Damascus last month.
Mr Kerry insisted Britain's decision not to back President Barack Obama in undertaking military strikes would not damage the special relationship between the countries. He insisted Washington had "no better partner" than the UK.
The Secretary of State said he appreciated the feelings of those on both sides of the Atlantic who are reluctant to get embroiled in Syria's two-and-a-half year civil war.
But he said: "It is important for us to stand up as nations for civility and against actions that challenge notions of humanity and decency and appropriate international behaviour.
"For almost 100 years, the world has stood together against the use of chemical weapons and we need to hear an appropriate outcry as we think back on those moments in history when large numbers of people have been killed because the world was silent: the Holocaust, Rwanda, and other moments are lessons to all of us today."
Mr Kerry was due back in Washington last night to brief Congress ahead of a White House address by Mr Obama today, which is designed to swing the Senate and House of Representatives towards backing military action in a series of votes over the coming weeks.
Mr Kerry said: "The United States of America - President Obama, myself and others - are in full agreement that the end of the conflict in Syria requires a political solution. There is no military solution and we have no illusions about that."
Mr Hague said the UK Government fully respects the decision of MPs not to back proposals in the Commons which would have paved the way to an eventual vote on British participation in a military strike on Assad.
But he stressed Britain would nonetheless continue to work to revive peace talks for Syria; to improve the world's humanitarian response; to support the moderate Syrian opposition; and to muster a strong international response to the deployment of chemical weapons.
Mr Hague urged more countries to sign up to the statement, supported by 11 states at last week's G20 conference, backing a strong international response to the use of chemical weapons.
Mr Kerry said: "The relationship between the US and UK has often been described as special or essential and it has been described thus simply because it is. It was before a vote the other day in parliament and it will be for long after that vote."