The presidential election still isn't over, but I can make one prediction that I feel confident about: at least 30% of the electorate will think it is the end of our country, and another 15% will be depressed until the first scandal hits the next administration.
My suggestion for solving this problem: Think about your most cherished social issue that is currently under dispute, such as same-sex marriage or abortion. First, ask yourself how far your views need to prevail in order for you to feel morally reconciled to the result. Your town? County? State? Or do you have to see your views enforced on the entire country (or world, for that matter) before you can sleep in peace at night?
Now ask yourself the converse. Presumably people on the opposite side of the issue feel as strongly as you do. How far are you willing to let them extend their interpretation if they are successful? Remember that the answer will be symmetric with the same answer that you gave above. If you will not rest until the whole country shares your views, you have to be prepared for the other side to insist on going equally far to enforce its views.
Now that you have thought about it from both perspectives, give your final answer. If you live in a state where 70% of the citizens share your views, can you live with not enforcing it on other states where 40% or fewer of the citizens agree with you? That is the principle of federalism, and the only way that national elections will cease to be such heart-rending issues is if we allow smaller, more homogeneous units to set their own policies. Yes, we are a single nation in many respects, but we are also deeply divided on many issues. Having a national defense policy makes a lot of sense; having a national policy on same-sex marriages or abortion makes a lot less sense. Until people come to accept that, they will have to live with the fact that there are going to be many angry people on one side or the other. And if the election doesn't go your way, it could be your side next week.