Winning the popular vote but losing the electoral college doesn’t mean the electors voted in opposition to the citizens of their state. The electoral college was put in place so large population centers wouldn’t carry more sway than states with more rural or agricultural areas. It was meant to provide equity between states. 

 Yes, and it (the Electroral College) is the only vote that counts for the Presidential election, per the Constitution.

If you can find anything about the popular vote in Article II, I'd be curious to see it.