In general, proteins do not work alone; they form macromolecular complexes to play fundamental roles in diverse cellular functions. On the basis of their iterative clustering procedure and frequency of occurrence in the macromolecular complexes, the protein subunits have been categorized as core and attachment. Core protein subunits are the main functional elements, whereas attachment proteins act as modifiers or activators in protein complexes. In this article, using the current data set of yeast protein complexes, we found that core proteins are evolving at a faster rate than attachment proteins in spite of their functional importance. Interestingly, our investigation revealed that attachment proteins are present in a higher number of macromolecular complexes than core proteins. We also observed that the protein complex number (defined as the number of protein complexes in which a protein subunit belongs) has a stronger influence on gene/protein essentiality than multifunctionality. Finally, our results suggest that the observed differences in the rates of protein evolution between core and attachment proteins are due to differences in protein complex number and expression level. Moreover, we conclude that proteins which are present in higher numbers of macromolecular complexes enhance their overall expression level by increasing their transcription rate as well as translation rate, and thus the protein complex number imposes a strong selection pressure on the evolution of yeast proteome.