Perspective is a strange thing. Perspective is nearly impossible to have in the moment and is generally gained the further away you are from the moment. The Mets and their fans would have been satisfied if you would have told them at the beginning of the year that they would make it to the World Series. However, after they just lost, or gave away, a very competitive series I am sure they are mighty upset.
As for the Royals, their tough World Series loss last year now looks like a building block to get them to this point. Last year at this time, they were cursing their third base coach and Bumgarner. Ahhh, perspective...
Perspective can even make me long for the A's playoff failures, in a season in which the playoffs felt so far away.
What can the A's take away from this? I think KC's bullpen has been the rock of their team. They had several comeback victories, but these were made possible by the bullpen keeping the other team scoreless. I think having that stellar bullpen gives the team confidence that they are in every game. Blowing late leads is the fastest way to kill confidence (see Oakland Athletics, 2015 season). KC's bullpen was basically developed in house, which is what the A's can focus on. I hate the idea of spending big money on relievers, because it usually doesn't work out. Draft, trade for, and develop all kinds of arms both for the rotation and the bullpen.
The offensive approach for the Royals was also unique. To my eye, it looked like they were all looking for fastballs and when they got one they pulled the trigger. The patient approach has also worked for teams, so I don't know that there is a one size fits all solution. The problem with being patient is that you usually watch many hittable pitches go by.