Qualitatively, electronegativity is a measure of how closely electrons are held in an atom. This allows us to give a qualitative theoretical explanation for your question.

In an s atomic orbital, electrons are allowed to get much closer to the nucleus -- and are therefore more tightly held -- than in a p atomic orbital. Hybrid orbitals (for carbon, sp, sp², sp³) are mixtures of an s atomic orbital with one, two or three p orbitals. As the p proportion of the mixture rises, the amount of "s-character" falls and the electrons in that orbital will be more loosely held by the central atom. Conversely, as the p-character falls, s-character rises and electrons will be more tightly held.

This means that electrons in an sp hybrid orbital are held more tightly than those in an sp² hybrid, which are in turn more tightly held than electrons in an sp³ hybrid orbital. So we say that the effective electronegativity of sp-hybridized carbon is higher than that of sp²-hybridized carbon, and sp³-hybridized carbon is lower than sp².

The power of this model is found both in bond strengths (C-H bond strengths go from about 99 kcal/mol in ethane to about 105 in ethene to about 111 in ethyne) and in the acidities of C-H bonds. When a C-H bond is deprotonated, the carbanion lone pair is held, according to the Pauling model, in a hybrid atomic orbital. More s-character means a more stable negative charge because the electrons are able to "snuggle" closer to the nucleus.

When we look at actual acidities, we find that ethyne is about 10¹⁰ times more acidic than ethene, which in turn is at least 10⁵ times more acidic than ethane.