Hardly anyone has a smaller school than homeschoolers and they do just fine with admissions. Did you take the most challenging coursework available to you? If possible, did you take some community college classes (or regular 4 year college)?
A high school student, whether in brick & mortar school or a homeschooler has just so many opportunities open to him/her. Kids in tiny private schools may not have the AP/IB program available and the SA's know that. A homeschooler may not have any chance to get to a college because of distance, time, or money, but if he has the internet in his home, there is a lot he can do.
The SA's want to see perseverance, inquisitiveness, leadership, determination, and pushing through attitude when faced with adversity.