You recently applied for a promotion position and wasn't selected, now the question is should you find another job? This happens everyday and there are a lot of things that have to be considered.
The first thing I will suggest is that you don't make a decision while being upset and angry.
If there was an interview process be honest with yourself about how you felt when you left the interview.
Was it a hard interview that you had trouble with or did you feel quite comfortable with your presentation? Regardless of how you feel you presented yourself request feedback from the board members, this is a fair request and a great company will gladly discuss it with you.
You also have to consider the other candidates as they may have been higher qualified and did a great presentation.
You can't develop an attitude of being cheated without requesting an evaluation.
I have interviewed thousands of people in my career and there are people that didn't do very well who were convinced they did great.
If you are given feedback then be open minded not defensive, ask for suggestions.
Take notes on these suggestions and accept them with sincerity.
If you have potential they will tell you that, there will be other opportunities in the future.
You also need to consider the history, vision and future of the company you are working for.
It wouldn't be a smart decision to take employment elsewhere that you haven't researched to find out they are going bankrupt.
I have seen applicant's interview for a supervisor position and do a stellar job but lose out to someone else.
In a short period of time another position was open and they were on the top of the list for consideration and were selected.
If you work for a great company don't necessarily quit until you are sure you don't fit in their future plans.