It was largely through the one-man campaign of a Polish jurist, Raphael Lemkin, someone who had lost family members in the Nazi holocaust, and who had invented the term "genocide", that the Resolution was adopted. [In Search of a Better World by Payam Akhavan p91-92]
The attitude at the time could be summed up in the words "Never again!" however the world would have to wait another 50 years before the International Criminal Court would be established to provide any real meaning to this Resolution.
See IBM and the Holocaust: The Strategic Alliance Between Nazi Germany and America's Most Powerful Corporation by Edwin Black. It is the stunning story of IBM's strategic alliance with Nazi Germany -- beginning in 1933 in the first weeks that Hitler came to power and continuing well into World War II. As the Third Reich embarked upon its plan of conquest and genocide, IBM and its subsidiaries helped create enabling technologies, step-by-step, from the identification and cataloging programs of the 1930s to the selections of the 1940s. A book review.