Theres a few things though that go in your favour - you have to take the good bits out of any situation like this.
They didn't say anything about you not having the intelligence for the job, thats good! At the end of the day, the essense of that sort of job is having the knowledge, and being able to advise etc.
Any interview experience is good experience.
I personally ask for feedback too, especially if you didn't get any really. Just say ''I know I haven't got the job, and will probably wont speak to you again (bit tongue in cheek - loosens them up though) but just wandering what I could have done better, or more what you would look for.''
A lot of the time, the jobs are earmarked for other people already (however not-right / immoral / illegal that may be). I once went to an interview for a company, put a lot of effort into reviewing them and their policies, as well as having done pretty much the exact job somewhere else before. I did well in the interview, and didnt get it. I asked for feedback, and the person who interviewed me gave me 5 minutes and said (Quote)
"You were probably the best person I've interviewed in the last few years, however, you stumbled on the last question and someone else nipped in ahead of you''
The last question was about equality and diversity. (1 out of 15 or so questions) To be honest with you, it didnt really relate to the job directly, and I dont know exactly how they wanted me to answer the question. I still gave them the year that their policy was introduced, how often it was maintained, and what it was about...... The person who got the job had never done it before either (and I just wandered how they could posibily do any better in an interview which I did near perfect?).. ANYWAY! /END RANT
Sorry I went off on that one, still niggles me. But the point was even though your'e the best candidate, theres other things in action too sometimes :/