AA was actually instituted to counter discrimination against Jews. Later, it was expanded to include other minorities who had been systematically disadvantaged (by those in power).
The justification for it is that minorities are still reeling from the effects of previous discriminatory policies, and AA used as a balancing force. Personally, I think if that's the issue, then we should use income based measures, not racially based ones.
Also, as someone else already pointed out, many racial groups are artificial. For example, there is a huge difference between a Filipino American and an international Chinese student, yet both are "Asian". There is also a huge difference between most Chinese Americans and Vietnamese Americans, who are mostly refugees from the Viet War. How can you classify all these diverse people with diverse backgrounds into one category? How does it help anything?
So yea, I agree some valuable resources are given to out undeservedly so, but only because we're using the wrong categories to measure who has been disadvantaged. I still agree with the spirit of AA, but not in its current form.