Hydrogen bonding doesn't occur with carbon. Brief rundown on hydrogen bonding -
Electronegativity is the tendency of an atom to attract electrons toward itself. When a highly electronegative atom, such as fluorine, nitrogen, or oxygen, bonds to hydrogen, you establish essentially a concentration gradient of electrons. The electronegative atom draws more bonding electrons toward itself than does the much less electronegative hydrogen. This creates an electric dipole. You end up with a partial positive charge on hydrogen and a partial negative charge on the electronegative atom. This molecule (positive charged on one end and negatively charged on the other) can interact with other similar molecules via electrostatic interactions (+ attracts -, and vice versa).
You could also view it by acid/base theory. When the hydrogen binds to the electronegative atom, due to the uneven sharing of electrons, it becomes moderately acidic, and the electronegative atom becomes moderately basic. You establish a network within the molecules of partial protonations/deprotonations.
This is why carbon isn't considered to take part in hydrogen bonding.
What Yggdrasil was saying can best be represented by the acid/base view. Bases are compounds with highly localized electron concentration. Because of resonance (delocalized charge), the oxygens are not as basic as they appear to be. They can still take part in hydrogen bonding to an extent however, assuming another molecule has a protic hydrogen (one attached to an electronegative atom).