The spell animate objects says:
Targets one Small object per caster level; see text
and
You may animate one Small or smaller object or a corresponding number of larger objects as follows: A Medium object counts as two Small or smaller objects, a Large object as four, a Huge object as eight, a Gargantuan object as 16, and a Colossal object as 32.
Therefore your caster level determines the size/number of animated objects you can create.
Per the table in the Animated Objects section of the Bestiary, that translates into CP based on size. So for you creating animated objects via the spell, those are the points you have to spend on special abilities for the constructs you make. If you're 12th level you can make, say, three Large objects (per the spell) each with 3 CP (per the Bestiary entry).
Now, the spell animate object is not the only way to get animated objects. They are also just plain monsters that a GM places. If a GM gives them a bunch more powers, then they should boost their CR. That's all that section that states "If an animated object spends more CP than its size category would allow" is saying. It's not directed to you, it's to the GM.
