You've raised one of the most difficult questions one can ask himself when presented with a similar situation but I think you handled the situation well. I often wonder how people with authority come up with the will to exercise their power when it affects so many lives and I wonder if I'll be able to do it if I were given the decision to make. Unfortunately my inexperience gives me no insight into myself. However, I'm inclined to accept that in most cases, there really isn't room for much emotion in business, especially if business is to be conducted efficiently. Not saying you must be an ass, but there is only so much you could do and while it's nice to express sympathy/empathy to those in desperation, there's sometimes nothing within your power to prevent it. Every person's gain is another's loss. When you hire someone, you're rejecting another applicant, when you give someone something, you are not giving it to someone else, that's the reality of a world of limited resources and the best you can hope for is that your difficult decision will be taken well and understood without a feeling of personal attachment. I suppose as an employee, it's to his or her benefit to understand that this decision making process is not an easy one and one that must be made. On the other hand as an employer, it may be your benefit to extend genuine care, in a professional manner of course, but without it leaving you with a lingering feeling of despair. As long as you can recognize the impact of your actions and handle the situation appropriately, there's no reason to beat yourself over it.
If you watch The Office, there was an episode in Season 1 where Michael contended for the entire duration of the episode on who to let go in the office. Ultimately he came to a decision but it was met with rebuttal by the person he layed off and he was kinda hurt by having to hurt someone else.
Your attachment to your humanity is a good thing, and I encourage you to seek more understanding of who you are and what you plan to do with yourself. However an unyielding grip can prevent you from achieving greater things. Hopefully you'll be able to come to a steady compromise.