I think it's okay to express gratitude. And other feelings, maybe. It just depends on how it's said, and whether you're self-centered about it or empathetic. It's like breaking up with someone. If an employee says that they enjoyed working with you and they're going to miss you, it's totally appropriate to respond in kind. Just don't whinge and draw all the attention to yourself.
In general I believe that there are no hard and fast rules about the expression of feelings in life. I agree that going on about all the emotional agony you went through to make the decision is worse than useless, but expressions of remorse like "I'm sorry it didn't work out" are totally fine in my opinion. A statement like "It's not personal, we had to make a business decision, and it wasn't easy." also communicates that the employee is not totally expendable, if that happens to be true, while also communicating personal concern.
By personal I meant for reasons not related to one's ability or importance to the company, such as being unlikable. Firing the worst performs is for professional reasons, not personal ones.
