Definitely. And keep in mind that this is maybe the most competitive year ever to get in because of a combination of: 1) the economic depression means less money available for the program and fewer slots as a result, 2) there are more applicants due to the slow economy (people trying to ride it out in school) plus historical trends indicating an increase in the number of clinical applicants every year anyway across the board.
So a rejection is normal and by no means a reflection of your ability or your standing relative to the rest of students. - For the most part, only the cream of the crop apply to a PhD program, and you're one of those. Even getting an invite to many places should be considered an achievement. Actually getting in = a combo of luck, fit, and interview ability.
But most all of us are perfectionists, overachievers and not used to failure/rejection EVER in our academic pursuits, much less a whole string of them. So it's going to hurt regardless.