[Taylor]

I think your second point was on target. With awards, it's not a matter of people losing them - that mindset is dangerous and poisonous. It's just that another team was able to leverage their resources very well, and they should be applauded. If that team is close to you, like the #1 seed was geographically and emotionally, perhaps this offseason you can work on things together and not only improve each other, but improve interteam connections.
Does your team have any large-scale projects coming up that could be shared among other groups to the benefit of all? (cough cough Red Stick Rumble sneeze)