It could be very important; it could be the deal breaker!
Have you ever received this kind of rejection message after you felt you slammed the interview? "Your credentials and experience were impressive, and you presented very well in the interview. In the end, the selected candidate had extensive experience that aligned better with the job and our company."
What they may be telling you is you did not convince them that your approach to the job and business is like theirs, that their business approach is in step with your own. You may have not made it clear to them that “we are alike”, or “you and I think alike”, or “I am aligned with you and your company”. It is worthwhile to convince them that, not only are you the best candidate, you have the same business interests and operating style.
Given two fairly equal candidates to choose from, one aligned the hiring manager and the other not aligned, that could greatly influence final choice.