Losing Game 7 in any round sucks. Given how difficult it is to make the final, as well as how infrequently most teams reach a final, it just magnifies the pain of falling short. It's like reading a good but hard to find book, and then when you reach the end you find out the last chapter is missing.
As a fan I speak from experience having seen my team lose game 7 in two of their 3 final appearances.
In 1994 it was heart break and sadness. In 2011 it was depression and a empty feeling. 2011 felt like a real gut punch, since that season it felt like we had done everything needed to win that year and yet still the same result in the end.
Tough losses like 2011 leave you struggling to keep trust and faith in the team no matter how well things are going since your always waiting for that other shoe to drop, and for them to find some way to blow it.