The main reaction that the US public had to the collapse of the Soviet Bloc was relief. We had been worried for so long about the possibility of nuclear war coming out of the Cold War. The collapse of the Soviet Bloc made it seem as if all the real danger in the world was gone. That was a huge change in our outlook.
A second reaction was the idea of the "peace dividend." What many people thought was that government spending on defense would be greatly reduced. We thought that the government would not need to keep up with the Soviets anymore and could either lower our taxes or spend the money on something more constructive than nuclear weapons.
Finally, there was certainly an element of triumph. It felt good because our way of life, which we thought was superior to the communist way of life, had won the war. It made us feel vindicated because it proved that we were better than the Soviets.