Its not only about quality (even if big part), but training. I see players who inferior players then us pass rings around our players when we face them. Genoa, Cagliari, Lazio just to mention a few have fantastic passing, while our approach is such that Momo has most passes for us.
Alot of it is the approach of the coach, and how he drills into his players to dictate and approach their game. Similar with Roma, likes of Perrotta, Taddei, Riise, Brighi, Tonetto arent really excellent passers, but been drilled into it with Spalletti's approach (Same with Allegri, Gasperini, Delio Rossi etc).